LMFDB - Embedded newform 240.2.bk.b.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(11,240)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("240.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bk (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	240.11
Dual form			240.2.bk.b.131.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.772787 - 1.18440i) q^{2} +(-0.112911 + 1.72837i) q^{3} +(-0.805601 + 1.83058i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.13433 - 1.20193i) q^{6} -2.33502 q^{7} +(2.79069 - 0.460493i) q^{8} +(-2.97450 - 0.390304i) q^{9} +O(q^{10})$	\(q+(-0.772787 - 1.18440i) q^{2} +(-0.112911 + 1.72837i) q^{3} +(-0.805601 + 1.83058i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.13433 - 1.20193i) q^{6} -2.33502 q^{7} +(2.79069 - 0.460493i) q^{8} +(-2.97450 - 0.390304i) q^{9} +(1.38394 + 0.291053i) q^{10} +(-4.04887 - 4.04887i) q^{11} +(-3.07294 - 1.59907i) q^{12} +(-0.834130 + 0.834130i) q^{13} +(1.80447 + 2.76560i) q^{14} +(-1.14230 - 1.30198i) q^{15} +(-2.70202 - 2.94943i) q^{16} +4.55545i q^{17} +(1.83638 + 3.82462i) q^{18} +(-3.99317 - 3.99317i) q^{19} +(-0.724767 - 1.86406i) q^{20} +(0.263650 - 4.03577i) q^{21} +(-1.66656 + 7.92440i) q^{22} +4.62939i q^{23} +(0.480800 + 4.87533i) q^{24} -1.00000i q^{25} +(1.63255 + 0.343338i) q^{26} +(1.01044 - 5.09696i) q^{27} +(1.88110 - 4.27443i) q^{28} +(4.29193 + 4.29193i) q^{29} +(-0.659309 + 2.35909i) q^{30} +6.62238i q^{31} +(-1.40521 + 5.47954i) q^{32} +(7.45510 - 6.54077i) q^{33} +(5.39547 - 3.52040i) q^{34} +(1.65111 - 1.65111i) q^{35} +(3.11074 - 5.13062i) q^{36} +(-1.12654 - 1.12654i) q^{37} +(-1.64364 + 7.81538i) q^{38} +(-1.34750 - 1.53586i) q^{39} +(-1.64770 + 2.29893i) q^{40} +1.26139 q^{41} +(-4.98371 + 2.80653i) q^{42} +(-5.15956 + 5.15956i) q^{43} +(10.6735 - 4.14999i) q^{44} +(2.37928 - 1.82730i) q^{45} +(5.48304 - 3.57753i) q^{46} +3.69227 q^{47} +(5.40278 - 4.33705i) q^{48} -1.54767 q^{49} +(-1.18440 + 0.772787i) q^{50} +(-7.87350 - 0.514362i) q^{51} +(-0.854962 - 2.19891i) q^{52} +(-4.30450 + 4.30450i) q^{53} +(-6.81769 + 2.74210i) q^{54} +5.72597 q^{55} +(-6.51632 + 1.07526i) q^{56} +(7.35254 - 6.45079i) q^{57} +(1.76661 - 8.40011i) q^{58} +(-8.10560 - 8.10560i) q^{59} +(3.30361 - 1.04219i) q^{60} +(7.50538 - 7.50538i) q^{61} +(7.84354 - 5.11769i) q^{62} +(6.94553 + 0.911368i) q^{63} +(7.57589 - 2.57018i) q^{64} -1.17964i q^{65} +(-13.5081 - 3.77519i) q^{66} +(2.85749 + 2.85749i) q^{67} +(-8.33911 - 3.66988i) q^{68} +(-8.00128 - 0.522709i) q^{69} +(-3.23153 - 0.679616i) q^{70} -9.41730i q^{71} +(-8.48064 + 0.280520i) q^{72} -0.435077i q^{73} +(-0.463696 + 2.20484i) q^{74} +(1.72837 + 0.112911i) q^{75} +(10.5267 - 4.09290i) q^{76} +(9.45421 + 9.45421i) q^{77} +(-0.777746 + 2.78287i) q^{78} +15.6995i q^{79} +(3.99617 + 0.174946i) q^{80} +(8.69533 + 2.32192i) q^{81} +(-0.974783 - 1.49398i) q^{82} +(-3.24036 + 3.24036i) q^{83} +(7.17539 + 3.73385i) q^{84} +(-3.22119 - 3.22119i) q^{85} +(10.0982 + 2.12373i) q^{86} +(-7.90264 + 6.93342i) q^{87} +(-13.1636 - 9.43467i) q^{88} +2.37976 q^{89} +(-4.00293 - 1.40590i) q^{90} +(1.94771 - 1.94771i) q^{91} +(-8.47444 - 3.72944i) q^{92} +(-11.4459 - 0.747740i) q^{93} +(-2.85333 - 4.37311i) q^{94} +5.64720 q^{95} +(-9.31199 - 3.04743i) q^{96} +7.06437 q^{97} +(1.19602 + 1.83306i) q^{98} +(10.4631 + 13.6237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.772787	−	1.18440i	−0.546443	−	0.837496i
$2$	−0.772787	−	1.18440i	−0.546443	−	0.837496i
$3$	−0.112911	+	1.72837i	−0.0651893	+	0.997873i
$3$	−0.112911	+	1.72837i	−0.0651893	+	0.997873i
$4$	−0.805601	+	1.83058i	−0.402800	+	0.915288i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	2.13433	−	1.20193i	0.871337	−	0.490685i
$7$	−2.33502			−0.882555			−0.441278	−	0.897371i	$-0.645475\pi$
$7$	−2.33502			−0.882555			−0.441278	+	0.897371i	$0.645475\pi$
$8$	2.79069	−	0.460493i	0.986658	−	0.162809i
$9$	−2.97450	−	0.390304i	−0.991501	−	0.130101i
$10$	1.38394	+	0.291053i	0.437640	+	0.0920392i
$11$	−4.04887	−	4.04887i	−1.22078	−	1.22078i	−0.967355	−	0.253426i	$-0.918442\pi$
$11$	−4.04887	−	4.04887i	−1.22078	−	1.22078i	−0.253426	−	0.967355i	$-0.581558\pi$
$12$	−3.07294	−	1.59907i	−0.887083	−	0.461610i
$13$	−0.834130	+	0.834130i	−0.231346	+	0.231346i	−0.813254	−	0.581908i	$-0.802306\pi$
$13$	−0.834130	+	0.834130i	−0.231346	+	0.231346i	0.581908	+	0.813254i	$0.302306\pi$
$14$	1.80447	+	2.76560i	0.482266	+	0.739137i
$15$	−1.14230	−	1.30198i	−0.294940	−	0.336170i
$16$	−2.70202	−	2.94943i	−0.675504	−	0.737357i
$17$			4.55545i			1.10486i	0.833559	+	0.552430i	$0.186299\pi$
$17$			4.55545i			1.10486i	−0.833559	+	0.552430i	$0.813701\pi$
$18$	1.83638	+	3.82462i	0.432839	+	0.901471i
$19$	−3.99317	−	3.99317i	−0.916097	−	0.916097i	0.0806463	−	0.996743i	$-0.474302\pi$
$19$	−3.99317	−	3.99317i	−0.916097	−	0.916097i	−0.996743	+	0.0806463i	$0.974302\pi$
$20$	−0.724767	−	1.86406i	−0.162063	−	0.416816i
$21$	0.263650	−	4.03577i	0.0575331	−	0.880678i
$22$	−1.66656	+	7.92440i	−0.355313	+	1.68949i
$23$			4.62939i			0.965294i	0.875815	+	0.482647i	$0.160325\pi$
$23$			4.62939i			0.965294i	−0.875815	+	0.482647i	$0.839675\pi$
$24$	0.480800	+	4.87533i	0.0981429	+	0.995172i
$25$		−	1.00000i		−	0.200000i
$26$	1.63255	+	0.343338i	0.320169	+	0.0673341i
$27$	1.01044	−	5.09696i	0.194460	−	0.980911i
$28$	1.88110	−	4.27443i	0.355494	−	0.807792i
$29$	4.29193	+	4.29193i	0.796992	+	0.796992i	0.982620	−	0.185628i	$-0.0594321\pi$
$29$	4.29193	+	4.29193i	0.796992	+	0.796992i	−0.185628	+	0.982620i	$0.559432\pi$
$30$	−0.659309	+	2.35909i	−0.120373	+	0.430709i
$31$			6.62238i			1.18941i	0.803942	+	0.594707i	$0.202732\pi$
$31$			6.62238i			1.18941i	−0.803942	+	0.594707i	$0.797268\pi$
$32$	−1.40521	+	5.47954i	−0.248409	+	0.968655i
$33$	7.45510	−	6.54077i	1.29777	−	1.13860i
$34$	5.39547	−	3.52040i	0.925316	−	0.603743i
$35$	1.65111	−	1.65111i	0.279089	−	0.279089i
$36$	3.11074	−	5.13062i	0.518457	−	0.855104i
$37$	−1.12654	−	1.12654i	−0.185202	−	0.185202i	0.608416	−	0.793618i	$-0.291805\pi$
$37$	−1.12654	−	1.12654i	−0.185202	−	0.185202i	−0.793618	+	0.608416i	$0.791805\pi$
$38$	−1.64364	+	7.81538i	−0.266633	+	1.26782i
$39$	−1.34750	−	1.53586i	−0.215773	−	0.245935i
$40$	−1.64770	+	2.29893i	−0.260524	+	0.363493i
$41$	1.26139			0.196996			0.0984978	−	0.995137i	$-0.468596\pi$
$41$	1.26139			0.196996			0.0984978	+	0.995137i	$0.468596\pi$
$42$	−4.98371	+	2.80653i	−0.769003	+	0.433056i
$43$	−5.15956	+	5.15956i	−0.786825	+	0.786825i	−0.980972	−	0.194147i	$-0.937806\pi$
$43$	−5.15956	+	5.15956i	−0.786825	+	0.786825i	0.194147	+	0.980972i	$0.437806\pi$
$44$	10.6735	−	4.14999i	1.60910	−	0.625635i
$45$	2.37928	−	1.82730i	0.354682	−	0.272398i
$46$	5.48304	−	3.57753i	0.808430	−	0.527478i
$47$	3.69227			0.538572			0.269286	−	0.963060i	$-0.413212\pi$
$47$	3.69227			0.538572			0.269286	+	0.963060i	$0.413212\pi$
$48$	5.40278	−	4.33705i	0.779824	−	0.625999i
$49$	−1.54767			−0.221096
$50$	−1.18440	+	0.772787i	−0.167499	+	0.109289i
$51$	−7.87350	−	0.514362i	−1.10251	−	0.0720250i
$52$	−0.854962	−	2.19891i	−0.118562	−	0.304934i
$53$	−4.30450	+	4.30450i	−0.591269	+	0.591269i	−0.937974	−	0.346705i	$-0.887301\pi$
$53$	−4.30450	+	4.30450i	−0.591269	+	0.591269i	0.346705	+	0.937974i	$0.387301\pi$
$54$	−6.81769	+	2.74210i	−0.927770	+	0.373152i
$55$	5.72597			0.772090
$56$	−6.51632	+	1.07526i	−0.870780	+	0.143688i
$57$	7.35254	−	6.45079i	0.973868	−	0.854428i
$58$	1.76661	−	8.40011i	0.231967	−	1.10299i
$59$	−8.10560	−	8.10560i	−1.05526	−	1.05526i	−0.998381	−	0.0568776i	$-0.981886\pi$
$59$	−8.10560	−	8.10560i	−1.05526	−	1.05526i	−0.0568776	−	0.998381i	$-0.518114\pi$
$60$	3.30361	−	1.04219i	0.426494	−	0.134546i
$61$	7.50538	−	7.50538i	0.960966	−	0.960966i	−0.0383004	−	0.999266i	$-0.512194\pi$
$61$	7.50538	−	7.50538i	0.960966	−	0.960966i	0.999266	+	0.0383004i	$0.0121944\pi$
$62$	7.84354	−	5.11769i	0.996130	−	0.649947i
$63$	6.94553	+	0.911368i	0.875054	+	0.114822i
$64$	7.57589	−	2.57018i	0.946987	−	0.321273i
$65$		−	1.17964i		−	0.146316i
$66$	−13.5081	−	3.77519i	−1.66273	−	0.464693i
$67$	2.85749	+	2.85749i	0.349098	+	0.349098i	0.859774	−	0.510675i	$-0.170605\pi$
$67$	2.85749	+	2.85749i	0.349098	+	0.349098i	−0.510675	+	0.859774i	$0.670605\pi$
$68$	−8.33911	−	3.66988i	−1.01127	−	0.445038i
$69$	−8.00128	−	0.522709i	−0.963241	−	0.0629268i
$70$	−3.23153	−	0.679616i	−0.386242	−	0.0812297i
$71$		−	9.41730i		−	1.11763i	−0.829293	−	0.558814i	$-0.811257\pi$
$71$		−	9.41730i		−	1.11763i	0.829293	−	0.558814i	$-0.188743\pi$
$72$	−8.48064	+	0.280520i	−0.999453	+	0.0330596i
$73$		−	0.435077i		−	0.0509219i	−0.999676	−	0.0254610i	$-0.991895\pi$
$73$		−	0.435077i		−	0.0509219i	0.999676	−	0.0254610i	$-0.00810535\pi$
$74$	−0.463696	+	2.20484i	−0.0539036	+	0.256308i
$75$	1.72837	+	0.112911i	0.199575	+	0.0130379i
$76$	10.5267	−	4.09290i	1.20750	−	0.469488i
$77$	9.45421	+	9.45421i	1.07741	+	1.07741i
$78$	−0.777746	+	2.78287i	−0.0880624	+	0.315098i
$79$			15.6995i			1.76633i	0.469065	+	0.883164i	$0.344591\pi$
$79$			15.6995i			1.76633i	−0.469065	+	0.883164i	$0.655409\pi$
$80$	3.99617	+	0.174946i	0.446786	+	0.0195596i
$81$	8.69533	+	2.32192i	0.966147	+	0.257991i
$82$	−0.974783	−	1.49398i	−0.107647	−	0.164983i
$83$	−3.24036	+	3.24036i	−0.355676	+	0.355676i	−0.862216	−	0.506541i	$-0.830924\pi$
$83$	−3.24036	+	3.24036i	−0.355676	+	0.355676i	0.506541	+	0.862216i	$0.330924\pi$
$84$	7.17539	+	3.73385i	0.782900	+	0.407397i
$85$	−3.22119	−	3.22119i	−0.349387	−	0.349387i
$86$	10.0982	+	2.12373i	1.08892	+	0.229008i
$87$	−7.90264	+	6.93342i	−0.847252	+	0.743341i
$88$	−13.1636	−	9.43467i	−1.40325	−	1.00574i
$89$	2.37976			0.252254			0.126127	−	0.992014i	$-0.459745\pi$
$89$	2.37976			0.252254			0.126127	+	0.992014i	$0.459745\pi$
$90$	−4.00293	−	1.40590i	−0.421946	−	0.148194i
$91$	1.94771	−	1.94771i	0.204176	−	0.204176i
$92$	−8.47444	−	3.72944i	−0.883522	−	0.388821i
$93$	−11.4459	−	0.747740i	−1.18688	−	0.0775370i
$94$	−2.85333	−	4.37311i	−0.294299	−	0.451052i
$95$	5.64720			0.579390
$96$	−9.31199	−	3.04743i	−0.950401	−	0.311027i
$97$	7.06437			0.717278			0.358639	−	0.933476i	$-0.383241\pi$
$97$	7.06437			0.717278			0.358639	+	0.933476i	$0.383241\pi$
$98$	1.19602	+	1.83306i	0.120816	+	0.185167i
$99$	10.4631	+	13.6237i	1.05158	+	1.36923i
$100$	1.83058	+	0.805601i	0.183058	+	0.0805601i
$101$	−1.17404	+	1.17404i	−0.116822	+	0.116822i	−0.763101	−	0.646279i	$-0.776324\pi$
$101$	−1.17404	+	1.17404i	−0.116822	+	0.116822i	0.646279	+	0.763101i	$0.276324\pi$
$102$	5.47533	+	9.72285i	0.542138	+	0.962706i
$103$	−9.75475			−0.961164			−0.480582	−	0.876950i	$-0.659575\pi$
$103$	−9.75475			−0.961164			−0.480582	+	0.876950i	$0.659575\pi$
$104$	−1.94369	+	2.71191i	−0.190594	+	0.265924i
$105$	2.66729	+	3.04015i	0.260301	+	0.296688i
$106$	8.42472	+	1.77178i	0.818281	+	0.172091i
$107$	8.14933	+	8.14933i	0.787826	+	0.787826i	0.981137	−	0.193312i	$-0.0619228\pi$
$107$	8.14933	+	8.14933i	0.787826	+	0.787826i	−0.193312	+	0.981137i	$0.561923\pi$
$108$	8.51636	+	5.95581i	0.819487	+	0.573098i
$109$	−11.3447	+	11.3447i	−1.08663	+	1.08663i	−0.0907523	+	0.995873i	$0.528927\pi$
$109$	−11.3447	+	11.3447i	−1.08663	+	1.08663i	−0.995873	+	0.0907523i	$0.971073\pi$
$110$	−4.42496	−	6.78183i	−0.421903	−	0.646622i
$111$	2.07427	−	1.81987i	0.196881	−	0.172735i
$112$	6.30926	+	6.88697i	0.596169	+	0.650758i
$113$		−	13.3697i		−	1.25771i	−0.777521	−	0.628857i	$-0.783523\pi$
$113$		−	13.3697i		−	1.25771i	0.777521	−	0.628857i	$-0.216477\pi$
$114$	−13.3223	−	3.72325i	−1.24774	−	0.348714i
$115$	−3.27347	−	3.27347i	−0.305253	−	0.305253i
$116$	−11.3143	+	4.39912i	−1.05051	+	0.408448i
$117$	2.80669	−	2.15556i	0.259478	−	0.199281i
$118$	−3.33636	+	15.8642i	−0.307137	+	1.46041i
$119$		−	10.6371i		−	0.975100i
$120$	−3.78736	−	3.10740i	−0.345737	−	0.283666i
$121$			21.7867i			1.98061i
$122$	−14.6894	−	3.08930i	−1.32992	−	0.279692i
$123$	−0.142425	+	2.18014i	−0.0128420	+	0.196576i
$124$	−12.1228	−	5.33499i	−1.08866	−	0.479096i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−4.28799	−	8.93057i	−0.382005	−	0.795598i
$127$			2.90551i			0.257822i	0.991656	+	0.128911i	$0.0411482\pi$
$127$			2.90551i			0.257822i	−0.991656	+	0.128911i	$0.958852\pi$
$128$	−8.89867	−	6.98667i	−0.786539	−	0.617541i
$129$	−8.33503	−	9.50018i	−0.733859	−	0.836444i
$130$	−1.39716	+	0.911609i	−0.122539	+	0.0799534i
$131$	−0.767498	+	0.767498i	−0.0670566	+	0.0670566i	−0.739840	−	0.672783i	$-0.765099\pi$
$131$	−0.767498	+	0.767498i	−0.0670566	+	0.0670566i	0.672783	+	0.739840i	$0.265099\pi$
$132$	5.96755	+	18.9164i	0.519408	+	1.64646i
$133$	9.32414	+	9.32414i	0.808506	+	0.808506i
$134$	1.17618	−	5.59264i	0.101606	−	0.483131i
$135$	2.88960	+	4.31859i	0.248698	+	0.371685i
$136$	2.09775	+	12.7129i	0.179881	+	1.09012i
$137$	−3.94052			−0.336661			−0.168331	−	0.985731i	$-0.553838\pi$
$137$	−3.94052			−0.336661			−0.168331	+	0.985731i	$0.553838\pi$
$138$	5.56419	+	9.88065i	0.473655	+	0.841096i
$139$	8.68502	−	8.68502i	0.736654	−	0.736654i	−0.235275	−	0.971929i	$-0.575599\pi$
$139$	8.68502	−	8.68502i	0.736654	−	0.736654i	0.971929	+	0.235275i	$0.0755992\pi$
$140$	1.69235	+	4.35262i	0.143029	+	0.367863i
$141$	−0.416898	+	6.38159i	−0.0351091	+	0.537427i
$142$	−11.1538	+	7.27757i	−0.936009	+	0.610720i
$143$	6.75457			0.564846
$144$	6.88598	+	9.82768i	0.573832	+	0.818973i
$145$	−6.06971			−0.504062
$146$	−0.515305	+	0.336222i	−0.0426469	+	0.0278259i
$147$	0.174749	−	2.67495i	0.0144131	−	0.220626i
$148$	2.96975	−	1.15467i	0.244112	−	0.0949135i
$149$	−8.32183	+	8.32183i	−0.681751	+	0.681751i	−0.960395	−	0.278644i	$-0.910115\pi$
$149$	−8.32183	+	8.32183i	−0.681751	+	0.681751i	0.278644	+	0.960395i	$0.410115\pi$
$150$	−1.20193	−	2.13433i	−0.0981370	−	0.174267i
$151$	8.10134			0.659278			0.329639	−	0.944107i	$-0.393073\pi$
$151$	8.10134			0.659278			0.329639	+	0.944107i	$0.393073\pi$
$152$	−12.9825	−	9.30488i	−1.05302	−	0.754725i
$153$	1.77801	−	13.5502i	0.143744	−	1.09547i
$154$	3.89146	−	18.5036i	0.313583	−	1.49107i
$155$	−4.68273	−	4.68273i	−0.376126	−	0.376126i
$156$	3.89706	−	1.22941i	0.312015	−	0.0984313i
$157$	2.81242	−	2.81242i	0.224456	−	0.224456i	−0.585916	−	0.810372i	$-0.699265\pi$
$157$	2.81242	−	2.81242i	0.224456	−	0.224456i	0.810372	+	0.585916i	$0.199265\pi$
$158$	18.5944	−	12.1323i	1.47929	−	0.965197i
$159$	−6.95374	−	7.92579i	−0.551467	−	0.628556i
$160$	−2.88098	−	4.86826i	−0.227762	−	0.384870i
$161$		−	10.8097i		−	0.851925i
$162$	−3.96956	−	12.0931i	−0.311878	−	0.950122i
$163$	−13.9627	−	13.9627i	−1.09364	−	1.09364i	−0.995137	−	0.0985042i	$-0.968594\pi$
$163$	−13.9627	−	13.9627i	−1.09364	−	1.09364i	−0.0985042	−	0.995137i	$-0.531406\pi$
$164$	−1.01617	+	2.30906i	−0.0793499	+	0.180308i
$165$	−0.646526	+	9.89658i	−0.0503320	+	0.770447i
$166$	6.34198	+	1.33377i	0.492233	+	0.103521i
$167$		−	4.67619i		−	0.361854i	−0.983497	−	0.180927i	$-0.942090\pi$
$167$		−	4.67619i		−	0.361854i	0.983497	−	0.180927i	$-0.0579098\pi$
$168$	−1.12268	−	11.3840i	−0.0866166	−	0.878295i
$169$			11.6085i			0.892958i
$170$	−1.32588	+	6.30447i	−0.101690	+	0.483531i
$171$	10.3191	+	13.4362i	0.789125	+	1.02750i
$172$	−5.28842	−	13.6015i	−0.403238	−	1.03710i
$173$	−8.34381	−	8.34381i	−0.634368	−	0.634368i	0.314792	−	0.949161i	$-0.398065\pi$
$173$	−8.34381	−	8.34381i	−0.634368	−	0.634368i	−0.949161	+	0.314792i	$0.898065\pi$
$174$	14.3190	+	4.00181i	1.08552	+	0.303377i
$175$			2.33502i			0.176511i
$176$	−1.00174	+	22.8820i	−0.0755086	+	1.72479i
$177$	14.9247	−	13.0942i	1.12181	−	0.984223i
$178$	−1.83905	−	2.81858i	−0.137842	−	0.211262i
$179$	11.2866	−	11.2866i	0.843598	−	0.843598i	−0.145727	−	0.989325i	$-0.546552\pi$
$179$	11.2866	−	11.2866i	0.843598	−	0.843598i	0.989325	+	0.145727i	$0.0465520\pi$
$180$	1.42827	+	5.82752i	0.106457	+	0.434358i
$181$	−13.4827	−	13.4827i	−1.00216	−	1.00216i	−0.999998	−	0.00216261i	$-0.999312\pi$
$181$	−13.4827	−	13.4827i	−1.00216	−	1.00216i	−0.00216261	−	0.999998i	$-0.500688\pi$
$182$	−3.81203	−	0.801701i	−0.282567	−	0.0594260i
$183$	12.1246	+	13.8195i	0.896277	+	1.02157i
$184$	2.13180	+	12.9192i	0.157158	+	0.952415i
$185$	1.59316			0.117132
$186$	7.95962	+	14.1343i	0.583627	+	1.03638i
$187$	18.4445	−	18.4445i	1.34879	−	1.34879i
$188$	−2.97449	+	6.75897i	−0.216937	+	0.492949i
$189$	−2.35940	+	11.9015i	−0.171621	+	0.865708i
$190$	−4.36408	−	6.68853i	−0.316604	−	0.485237i
$191$	−13.8582			−1.00274			−0.501371	−	0.865232i	$-0.667171\pi$
$191$	−13.8582			−1.00274			−0.501371	+	0.865232i	$0.667171\pi$
$192$	3.58682	+	13.3841i	0.258856	+	0.965916i
$193$	−21.0706			−1.51669			−0.758346	−	0.651852i	$-0.773992\pi$
$193$	−21.0706			−1.51669			−0.758346	+	0.651852i	$0.773992\pi$
$194$	−5.45925	−	8.36703i	−0.391952	−	0.600718i
$195$	2.03885	+	0.133194i	0.146005	+	0.00953824i
$196$	1.24681	−	2.83313i	0.0890576	−	0.202367i
$197$	−1.32560	+	1.32560i	−0.0944450	+	0.0944450i	−0.752751	−	0.658306i	$-0.771273\pi$
$197$	−1.32560	+	1.32560i	−0.0944450	+	0.0944450i	0.658306	+	0.752751i	$0.271273\pi$
$198$	8.05012	−	22.9207i	0.572097	−	1.62890i
$199$	8.01961			0.568495			0.284248	−	0.958751i	$-0.408256\pi$
$199$	8.01961			0.568495			0.284248	+	0.958751i	$0.408256\pi$
$200$	−0.460493	−	2.79069i	−0.0325617	−	0.197332i
$201$	−5.26144	+	4.61615i	−0.371113	+	0.325598i
$202$	2.29782	+	0.483250i	0.161674	+	0.0340014i
$203$	−10.0218	−	10.0218i	−0.703389	−	0.703389i
$204$	7.28447	−	13.9987i	0.510015	−	0.980102i
$205$	−0.891935	+	0.891935i	−0.0622954	+	0.0622954i
$206$	7.53834	+	11.5535i	0.525221	+	0.804971i
$207$	1.80687	−	13.7701i	0.125586	−	0.957090i
$208$	4.71404	+	0.206373i	0.326860	+	0.0143094i
$209$			32.3357i			2.23671i
$210$	1.53950	−	5.50853i	0.106236	−	0.380125i
$211$	−9.19540	−	9.19540i	−0.633037	−	0.633037i	0.315791	−	0.948829i	$-0.397730\pi$
$211$	−9.19540	−	9.19540i	−0.633037	−	0.633037i	−0.948829	+	0.315791i	$0.897730\pi$
$212$	−4.41201	−	11.3474i	−0.303018	−	0.779345i
$213$	16.2765	+	1.06332i	1.11525	+	0.0728573i
$214$	3.35436	−	15.9498i	0.229299	−	1.09030i
$215$		−	7.29672i		−	0.497632i
$216$	0.472717	−	14.6893i	0.0321643	−	0.999483i
$217$		−	15.4634i		−	1.04972i
$218$	22.2037	+	4.66961i	1.50382	+	0.316266i
$219$	0.751973	+	0.0491251i	0.0508136	+	0.00331956i
$220$	−4.61285	+	10.4818i	−0.310998	+	0.706684i
$221$	−3.79984	−	3.79984i	−0.255605	−	0.255605i
$222$	−3.75842	−	1.05039i	−0.252249	−	0.0704974i
$223$		−	10.4693i		−	0.701077i	−0.936548	−	0.350538i	$-0.885999\pi$
$223$		−	10.4693i		−	0.701077i	0.936548	−	0.350538i	$-0.114001\pi$
$224$	3.28121	−	12.7948i	0.219235	−	0.854892i
$225$	−0.390304	+	2.97450i	−0.0260202	+	0.198300i
$226$	−15.8350	+	10.3319i	−1.05333	+	0.687268i
$227$	−9.14639	+	9.14639i	−0.607067	+	0.607067i	−0.942178	−	0.335112i	$-0.891226\pi$
$227$	−9.14639	+	9.14639i	−0.607067	+	0.607067i	0.335112	+	0.942178i	$0.391226\pi$
$228$	5.88545	+	18.6561i	0.389774	+	1.23553i
$229$	4.20638	+	4.20638i	0.277965	+	0.277965i	0.832296	−	0.554331i	$-0.187026\pi$
$229$	4.20638	+	4.20638i	0.277965	+	0.277965i	−0.554331	+	0.832296i	$0.687026\pi$
$230$	−1.34740	+	6.40679i	−0.0888449	+	0.422451i
$231$	−17.4078	+	15.2729i	−1.14535	+	1.00488i
$232$	13.9538	+	10.0010i	0.916115	+	0.656601i
$233$	12.0946			0.792341			0.396170	−	0.918177i	$-0.370339\pi$
$233$	12.0946			0.792341			0.396170	+	0.918177i	$0.370339\pi$
$234$	−4.72201	−	1.65845i	−0.308687	−	0.108416i
$235$	−2.61083	+	2.61083i	−0.170312	+	0.170312i
$236$	21.3678	−	8.30803i	1.39092	−	0.540807i
$237$	−27.1344	−	1.77264i	−1.76257	−	0.115146i
$238$	−12.5986	+	8.22020i	−0.816643	+	0.532837i
$239$	7.62398			0.493154			0.246577	−	0.969123i	$-0.420694\pi$
$239$	7.62398			0.493154			0.246577	+	0.969123i	$0.420694\pi$
$240$	−0.753583	+	6.88710i	−0.0486436	+	0.444560i
$241$	6.89332			0.444038			0.222019	−	0.975042i	$-0.428735\pi$
$241$	6.89332			0.444038			0.222019	+	0.975042i	$0.428735\pi$
$242$	25.8042	−	16.8365i	1.65876	−	1.08229i
$243$	−4.99492	+	14.7665i	−0.320425	+	0.947274i
$244$	7.69283	+	19.7855i	0.492483	+	1.26664i
$245$	1.09437	−	1.09437i	0.0699167	−	0.0699167i
$246$	2.69222	−	1.51610i	0.171650	−	0.0966627i
$247$	6.66165			0.423871
$248$	3.04956	+	18.4810i	0.193647	+	1.17354i
$249$	−5.23465	−	5.96640i	−0.331733	−	0.378105i
$250$	0.291053	−	1.38394i	0.0184078	−	0.0875280i
$251$	19.4059	+	19.4059i	1.22489	+	1.22489i	0.965874	+	0.259014i	$0.0833975\pi$
$251$	19.4059	+	19.4059i	1.22489	+	1.22489i	0.259014	+	0.965874i	$0.416603\pi$
$252$	−7.26365	+	11.9801i	−0.457567	+	0.754676i
$253$	18.7438	−	18.7438i	1.17841	−	1.17841i
$254$	3.44128	−	2.24534i	0.215925	−	0.140885i
$255$	5.93111	−	5.20369i	0.371421	−	0.325868i
$256$	−1.39823	+	15.9388i	−0.0873893	+	0.996174i
$257$		−	0.630711i		−	0.0393427i	−0.999807	−	0.0196713i	$-0.993738\pi$
$257$		−	0.630711i		−	0.0393427i	0.999807	−	0.0196713i	$-0.00626198\pi$
$258$	−4.81079	+	17.2136i	−0.299507	+	1.07167i
$259$	2.63049	+	2.63049i	0.163451	+	0.163451i
$260$	2.15942	+	0.950317i	0.133921	+	0.0589362i
$261$	−11.0912	−	14.4415i	−0.686528	−	0.893907i
$262$	1.50214	+	0.315911i	0.0928023	+	0.0195171i
$263$			26.0577i			1.60679i	0.595448	+	0.803394i	$0.296974\pi$
$263$			26.0577i			1.60679i	−0.595448	+	0.803394i	$0.703026\pi$
$264$	17.7929	−	21.6863i	1.09508	−	1.33470i
$265$		−	6.08749i		−	0.373951i
$266$	3.83793	−	18.2491i	0.235318	−	1.11892i
$267$	−0.268701	+	4.11309i	−0.0164442	+	0.251717i
$268$	−7.53285	+	2.92886i	−0.460142	+	0.178908i
$269$	−14.3628	−	14.3628i	−0.875714	−	0.875714i	0.117374	−	0.993088i	$-0.462552\pi$
$269$	−14.3628	−	14.3628i	−0.875714	−	0.875714i	−0.993088	+	0.117374i	$0.962552\pi$
$270$	2.88188	−	6.75979i	0.175386	−	0.411388i
$271$			9.19991i			0.558855i	0.960167	+	0.279427i	$0.0901446\pi$
$271$			9.19991i			0.558855i	−0.960167	+	0.279427i	$0.909855\pi$
$272$	13.4360	−	12.3089i	0.814676	−	0.746337i
$273$	3.14644	+	3.58628i	0.190431	+	0.217051i
$274$	3.04518	+	4.66715i	0.183966	+	0.281953i
$275$	−4.04887	+	4.04887i	−0.244156	+	0.244156i
$276$	7.40269	−	14.2258i	0.445590	−	0.856295i
$277$	−5.81216	−	5.81216i	−0.349219	−	0.349219i	0.510600	−	0.859819i	$-0.329423\pi$
$277$	−5.81216	−	5.81216i	−0.349219	−	0.349219i	−0.859819	+	0.510600i	$0.829423\pi$
$278$	−16.9982	−	3.57486i	−1.01948	−	0.214406i
$279$	2.58474	−	19.6983i	0.154744	−	1.17931i
$280$	3.84741	−	5.36806i	0.229927	−	0.320803i
$281$	−17.6560			−1.05327			−0.526634	−	0.850092i	$-0.676546\pi$
$281$	−17.6560			−1.05327			−0.526634	+	0.850092i	$0.676546\pi$
$282$	7.88052	−	4.43784i	0.469278	−	0.264269i
$283$	−11.0458	+	11.0458i	−0.656604	+	0.656604i	−0.954575	−	0.297971i	$-0.903690\pi$
$283$	−11.0458	+	11.0458i	−0.656604	+	0.656604i	0.297971	+	0.954575i	$0.403690\pi$
$284$	17.2391	+	7.58658i	1.02295	+	0.450181i
$285$	−0.637631	+	9.76043i	−0.0377700	+	0.578158i
$286$	−5.21985	−	8.00011i	−0.308656	−	0.473056i
$287$	−2.94537			−0.173859
$288$	6.31850	−	15.7504i	0.372321	−	0.928104i
$289$	−3.75217			−0.220716
$290$	4.69059	+	7.18895i	0.275441	+	0.422150i
$291$	−0.797646	+	12.2098i	−0.0467588	+	0.715752i
$292$	0.796442	+	0.350499i	0.0466082	+	0.0205114i
$293$	−13.0705	+	13.0705i	−0.763584	+	0.763584i	−0.976968	−	0.213384i	$-0.931551\pi$
$293$	−13.0705	+	13.0705i	−0.763584	+	0.763584i	0.213384	+	0.976968i	$0.431551\pi$
$294$	−3.30325	+	1.86019i	−0.192649	+	0.108488i
$295$	11.4630			0.667404
$296$	−3.66258	−	2.62505i	−0.212883	−	0.152578i
$297$	−24.7281	+	16.5458i	−1.43487	+	0.960084i
$298$	16.2874	+	3.42536i	0.943502	+	0.198426i
$299$	−3.86151	−	3.86151i	−0.223317	−	0.223317i
$300$	−1.59907	+	3.07294i	−0.0923221	+	0.177417i
$301$	12.0477	−	12.0477i	0.694417	−	0.694417i
$302$	−6.26061	−	9.59521i	−0.360258	−	0.552143i
$303$	−1.89662	−	2.16174i	−0.108958	−	0.124189i
$304$	−0.987954	+	22.5672i	−0.0566631	+	1.29432i
$305$			10.6142i			0.607768i
$306$	−17.4229	+	8.36555i	−0.995999	+	0.478227i
$307$	4.54167	+	4.54167i	0.259207	+	0.259207i	0.824731	−	0.565525i	$-0.191326\pi$
$307$	4.54167	+	4.54167i	0.259207	+	0.259207i	−0.565525	+	0.824731i	$0.691326\pi$
$308$	−24.9230	+	9.69033i	−1.42012	+	0.552158i
$309$	1.10142	−	16.8598i	0.0626576	−	0.959120i
$310$	−1.92747	+	9.16497i	−0.109473	+	0.520535i
$311$		−	6.61127i		−	0.374891i	−0.982275	−	0.187445i	$-0.939979\pi$
$311$		−	6.61127i		−	0.374891i	0.982275	−	0.187445i	$-0.0600207\pi$
$312$	−4.46771	−	3.66561i	−0.252934	−	0.207524i
$313$		−	4.90590i		−	0.277298i	−0.990342	−	0.138649i	$-0.955724\pi$
$313$		−	4.90590i		−	0.277298i	0.990342	−	0.138649i	$-0.0442760\pi$
$314$	−5.50443	−	1.15763i	−0.310633	−	0.0653286i
$315$	−5.55566	+	4.26680i	−0.313026	+	0.240407i
$316$	−28.7390	−	12.6475i	−1.61670	−	0.711477i
$317$	4.98437	+	4.98437i	0.279950	+	0.279950i	0.833089	−	0.553139i	$-0.186570\pi$
$317$	4.98437	+	4.98437i	0.279950	+	0.279950i	−0.553139	+	0.833089i	$0.686570\pi$
$318$	−4.01354	+	14.3609i	−0.225068	+	0.805322i
$319$		−	34.7550i		−	1.94590i
$320$	−3.53957	+	7.17436i	−0.197868	+	0.401059i
$321$	−15.0052	+	13.1649i	−0.837508	+	0.734792i
$322$	−12.8030	+	8.35361i	−0.713484	+	0.465528i
$323$	18.1907	−	18.1907i	1.01216	−	1.01216i
$324$	−11.2554	+	14.0469i	−0.625300	+	0.780384i
$325$	0.834130	+	0.834130i	0.0462692	+	0.0462692i
$326$	−5.74720	+	27.3275i	−0.318308	+	1.51353i
$327$	−18.3269	−	20.8888i	−1.01348	−	1.15515i
$328$	3.52014	−	0.580859i	0.194367	−	0.0320726i
$329$	−8.62152			−0.475320
$330$	12.2211	−	6.88220i	0.672750	−	0.378853i
$331$	3.16037	−	3.16037i	0.173710	−	0.173710i	−0.614898	−	0.788607i	$-0.710803\pi$
$331$	3.16037	−	3.16037i	0.173710	−	0.173710i	0.788607	+	0.614898i	$0.210803\pi$
$332$	−3.32129	−	8.54216i	−0.182279	−	0.468812i
$333$	2.91120	+	3.79058i	0.159533	+	0.207723i
$334$	−5.53847	+	3.61370i	−0.303052	+	0.197733i
$335$	−4.04110			−0.220789
$336$	−12.6156	+	10.1271i	−0.688238	+	0.552479i
$337$	−27.2432			−1.48403			−0.742016	−	0.670382i	$-0.766130\pi$
$337$	−27.2432			−1.48403			−0.742016	+	0.670382i	$0.766130\pi$
$338$	13.7490	−	8.97086i	0.747849	−	0.487951i
$339$	23.1077	+	1.50958i	1.25504	+	0.0819894i
$340$	8.49163	−	3.30164i	0.460523	−	0.179057i
$341$	26.8132	−	26.8132i	1.45201	−	1.45201i
$342$	7.93937	−	22.6053i	0.429312	−	1.22236i
$343$	19.9590			1.07768
$344$	−12.0228	+	16.7747i	−0.648225	+	0.904429i
$345$	6.02737	−	5.28815i	0.324503	−	0.284704i
$346$	−3.43441	+	16.3304i	−0.184635	+	0.877927i
$347$	2.00841	+	2.00841i	0.107817	+	0.107817i	0.758957	−	0.651140i	$-0.225709\pi$
$347$	2.00841	+	2.00841i	0.107817	+	0.107817i	−0.651140	+	0.758957i	$0.725709\pi$
$348$	−6.32579	−	20.0519i	−0.339098	−	1.07490i
$349$	15.7596	−	15.7596i	0.843592	−	0.843592i	−0.145732	−	0.989324i	$-0.546554\pi$
$349$	15.7596	−	15.7596i	0.843592	−	0.843592i	0.989324	+	0.145732i	$0.0465536\pi$
$350$	2.76560	−	1.80447i	0.147827	−	0.0964532i
$351$	3.40869	+	5.09437i	0.181942	+	0.271917i
$352$	27.8755	−	16.4964i	1.48577	−	0.879263i
$353$		−	13.9552i		−	0.742761i	−0.928481	−	0.371380i	$-0.878885\pi$
$353$		−	13.9552i		−	0.742761i	0.928481	−	0.371380i	$-0.121115\pi$
$354$	−27.0424	−	7.55769i	−1.43729	−	0.401687i
$355$	6.65904	+	6.65904i	0.353425	+	0.353425i
$356$	−1.91713	+	4.35633i	−0.101608	+	0.230885i
$357$	18.3848	+	1.20105i	0.973026	+	0.0635661i
$358$	−22.0899	−	4.64569i	−1.16749	−	0.245532i
$359$			17.2382i			0.909798i	0.890543	+	0.454899i	$0.150325\pi$
$359$			17.2382i			0.909798i	−0.890543	+	0.454899i	$0.849675\pi$
$360$	5.79836	−	6.19508i	0.305601	−	0.326509i
$361$			12.8908i			0.678466i
$362$	−5.54963	+	26.3881i	−0.291682	+	1.38693i
$363$	−37.6555	−	2.45997i	−1.97640	−	0.129115i
$364$	1.99636	+	5.13451i	0.104637	+	0.269122i
$365$	0.307646	+	0.307646i	0.0161029	+	0.0161029i
$366$	6.99805	−	25.0399i	0.365794	−	1.30886i
$367$			27.4809i			1.43449i	0.696820	+	0.717246i	$0.254598\pi$
$367$			27.4809i			1.43449i	−0.696820	+	0.717246i	$0.745402\pi$
$368$	13.6540	−	12.5087i	0.711766	−	0.652060i
$369$	−3.75200	−	0.492324i	−0.195321	−	0.0256294i
$370$	−1.23118	−	1.88694i	−0.0640058	−	0.0980975i
$371$	10.0511	−	10.0511i	0.521828	−	0.521828i
$372$	10.5896	−	20.3502i	0.549046	−	1.05511i
$373$	21.8128	+	21.8128i	1.12942	+	1.12942i	0.990271	+	0.139152i	$0.0444376\pi$
$373$	21.8128	+	21.8128i	1.12942	+	1.12942i	0.139152	+	0.990271i	$0.455562\pi$
$374$	−36.0992	−	7.59196i	−1.86665	−	0.392571i
$375$	−1.30198	+	1.14230i	−0.0672340	+	0.0589881i
$376$	10.3040	−	1.70026i	0.531387	−	0.0876843i
$377$	−7.16006			−0.368762
$378$	15.9195	−	6.40286i	0.818808	−	0.329328i
$379$	−2.07971	+	2.07971i	−0.106828	+	0.106828i	−0.758500	−	0.651673i	$-0.774068\pi$
$379$	−2.07971	+	2.07971i	−0.106828	+	0.106828i	0.651673	+	0.758500i	$0.274068\pi$
$380$	−4.54939	+	10.3376i	−0.233379	+	0.530309i
$381$	−5.02179	−	0.328064i	−0.257274	−	0.0168073i
$382$	10.7094	+	16.4136i	0.547941	+	0.839793i
$383$	−22.2477			−1.13681			−0.568403	−	0.822750i	$-0.692439\pi$
$383$	−22.2477			−1.13681			−0.568403	+	0.822750i	$0.692439\pi$
$384$	13.0803	−	14.5913i	0.667501	−	0.744609i
$385$	−13.3703			−0.681412
$386$	16.2831	+	24.9559i	0.828786	+	1.27022i
$387$	17.3609	−	13.3333i	0.882505	−	0.677771i
$388$	−5.69106	+	12.9319i	−0.288920	+	0.656516i
$389$	14.3518	−	14.3518i	0.727667	−	0.727667i	−0.242488	−	0.970154i	$-0.577963\pi$
$389$	14.3518	−	14.3518i	0.727667	−	0.727667i	0.970154	+	0.242488i	$0.0779634\pi$
$390$	−1.41784	−	2.51774i	−0.0717951	−	0.127491i
$391$	−21.0890			−1.06651
$392$	−4.31907	+	0.712692i	−0.218146	+	0.0359964i
$393$	−1.23986	−	1.41318i	−0.0625426	−	0.0712854i
$394$	2.59444	+	0.545632i	0.130706	+	0.0274885i
$395$	−11.1012	−	11.1012i	−0.558562	−	0.558562i
$396$	−33.3682	+	8.17824i	−1.67682	+	0.410972i
$397$	9.21181	−	9.21181i	0.462328	−	0.462328i	−0.437090	−	0.899418i	$-0.643991\pi$
$397$	9.21181	−	9.21181i	0.462328	−	0.462328i	0.899418	+	0.437090i	$0.143991\pi$
$398$	−6.19745	−	9.49841i	−0.310650	−	0.476113i
$399$	−17.1683	+	15.0627i	−0.859492	+	0.754080i
$400$	−2.94943	+	2.70202i	−0.147471	+	0.135101i
$401$			9.32535i			0.465686i	0.972514	+	0.232843i	$0.0748028\pi$
$401$			9.32535i			0.465686i	−0.972514	+	0.232843i	$0.925197\pi$
$402$	9.53333	+	2.66434i	0.475479	+	0.132885i
$403$	−5.52392	−	5.52392i	−0.275166	−	0.275166i
$404$	−1.20337	−	3.09499i	−0.0598697	−	0.153981i
$405$	−7.79037	+	4.50668i	−0.387106	+	0.223939i
$406$	−4.12507	+	19.6144i	−0.204724	+	0.973448i
$407$			9.12241i			0.452181i
$408$	−22.2093	+	2.19026i	−1.09953	+	0.108434i
$409$		−	17.7939i		−	0.879850i	−0.898035	−	0.439925i	$-0.855005\pi$
$409$		−	17.7939i		−	0.879850i	0.898035	−	0.439925i	$-0.144995\pi$
$410$	1.74568	+	0.367131i	0.0862131	+	0.0181313i
$411$	0.444928	−	6.81066i	0.0219467	−	0.335945i
$412$	7.85843	−	17.8568i	0.387157	−	0.879742i
$413$	18.9267	+	18.9267i	0.931324	+	0.931324i
$414$	−17.7056	+	8.50132i	−0.870185	+	0.417817i
$415$		−	4.58256i		−	0.224949i
$416$	−3.39852	−	5.74278i	−0.166626	−	0.281563i
$417$	14.0303	+	15.9915i	0.687065	+	0.783109i
$418$	38.2984	−	24.9886i	1.87323	−	1.22223i
$419$	−24.3854	+	24.3854i	−1.19130	+	1.19130i	−0.214601	+	0.976702i	$0.568845\pi$
$419$	−24.3854	+	24.3854i	−1.19130	+	1.19130i	−0.976702	+	0.214601i	$0.931155\pi$
$420$	−7.71400	+	2.43354i	−0.376405	+	0.118744i
$421$	26.3102	+	26.3102i	1.28228	+	1.28228i	0.939366	+	0.342917i	$0.111415\pi$
$421$	26.3102	+	26.3102i	1.28228	+	1.28228i	0.342917	+	0.939366i	$0.388585\pi$
$422$	−3.78493	+	17.9971i	−0.184248	+	0.876085i
$423$	−10.9827	−	1.44110i	−0.533995	−	0.0700689i
$424$	−10.0303	+	13.9947i	−0.487117	+	0.679644i
$425$	4.55545			0.220972
$426$	−11.3189	−	20.0996i	−0.548403	−	0.973831i
$427$	−17.5252	+	17.5252i	−0.848106	+	0.848106i
$428$	−21.4831	+	8.35286i	−1.03842	+	0.403751i
$429$	−0.762666	+	11.6744i	−0.0368219	+	0.563644i
$430$	−8.64222	+	5.63881i	−0.416765	+	0.271927i
$431$	5.13200			0.247200			0.123600	−	0.992332i	$-0.460556\pi$
$431$	5.13200			0.247200			0.123600	+	0.992332i	$0.460556\pi$
$432$	−17.7633	+	10.7918i	−0.854639	+	0.519223i
$433$	25.8271			1.24117			0.620586	−	0.784138i	$-0.286895\pi$
$433$	25.8271			1.24117			0.620586	+	0.784138i	$0.286895\pi$
$434$	−18.3148	+	11.9499i	−0.879140	+	0.573614i
$435$	0.685337	−	10.4907i	0.0328594	−	0.502990i
$436$	−11.6280	−	29.9066i	−0.556882	−	1.43227i
$437$	18.4859	−	18.4859i	0.884302	−	0.884302i
$438$	−0.522931	−	0.928599i	−0.0249866	−	0.0443702i
$439$	−6.56874			−0.313509			−0.156755	−	0.987638i	$-0.550103\pi$
$439$	−6.56874			−0.313509			−0.156755	+	0.987638i	$0.550103\pi$
$440$	15.9794	−	2.63677i	0.761788	−	0.125703i
$441$	4.60355	+	0.604062i	0.219217	+	0.0287649i
$442$	−1.56406	+	7.43700i	−0.0743947	+	0.353742i
$443$	22.2932	+	22.2932i	1.05918	+	1.05918i	0.998135	+	0.0610464i	$0.0194437\pi$
$443$	22.2932	+	22.2932i	1.05918	+	1.05918i	0.0610464	+	0.998135i	$0.480556\pi$
$444$	1.66038	+	5.26320i	0.0787982	+	0.249780i
$445$	−1.68274	+	1.68274i	−0.0797697	+	0.0797697i
$446$	−12.3998	+	8.09055i	−0.587149	+	0.383098i
$447$	−13.4435	−	15.3228i	−0.635858	−	0.724744i
$448$	−17.6899	+	6.00144i	−0.835768	+	0.283541i
$449$			19.7304i			0.931133i	0.885013	+	0.465566i	$0.154149\pi$
$449$			19.7304i			0.931133i	−0.885013	+	0.465566i	$0.845851\pi$
$450$	3.82462	−	1.83638i	0.180294	−	0.0865678i
$451$	−5.10719	−	5.10719i	−0.240488	−	0.240488i
$452$	24.4742	+	10.7706i	1.15117	+	0.506607i
$453$	−0.914731	+	14.0021i	−0.0429778	+	0.657875i
$454$	17.9012	+	3.76476i	0.840144	+	0.176689i
$455$			2.75448i			0.129132i
$456$	17.5481	−	21.3879i	0.821765	−	1.00158i
$457$			25.6189i			1.19840i	0.800599	+	0.599201i	$0.204515\pi$
$457$			25.6189i			1.19840i	−0.800599	+	0.599201i	$0.795485\pi$
$458$	1.73140	−	8.23267i	0.0809028	−	0.384687i
$459$	23.2190	+	4.60302i	1.08377	+	0.214851i
$460$	8.62945	−	3.35523i	0.402350	−	0.156438i
$461$	−13.1368	−	13.1368i	−0.611841	−	0.611841i	0.331585	−	0.943425i	$-0.392417\pi$
$461$	−13.1368	−	13.1368i	−0.611841	−	0.611841i	−0.943425	+	0.331585i	$0.892417\pi$
$462$	31.5417	+	8.81514i	1.46745	+	0.410117i
$463$		−	13.7820i		−	0.640502i	−0.947333	−	0.320251i	$-0.896233\pi$
$463$		−	13.7820i		−	0.640502i	0.947333	−	0.320251i	$-0.103767\pi$
$464$	1.06187	−	24.2556i	0.0492961	−	1.12604i
$465$	8.62220	−	7.56474i	0.399845	−	0.350806i
$466$	−9.34652	−	14.3248i	−0.432969	−	0.663582i
$467$	2.88901	−	2.88901i	0.133687	−	0.133687i	−0.637097	−	0.770784i	$-0.719865\pi$
$467$	2.88901	−	2.88901i	0.133687	−	0.133687i	0.770784	+	0.637097i	$0.219865\pi$
$468$	1.68484	+	6.87437i	0.0778819	+	0.317768i
$469$	−6.67231	−	6.67231i	−0.308099	−	0.308099i
$470$	5.10987	+	1.07465i	0.235701	+	0.0495698i
$471$	4.54334	+	5.17845i	0.209346	+	0.238610i
$472$	−26.3528	−	18.8876i	−1.21298	−	0.869374i
$473$	41.7808			1.92108
$474$	18.8696	+	33.5078i	0.866710	+	1.53907i
$475$	−3.99317	+	3.99317i	−0.183219	+	0.183219i
$476$	19.4720	+	8.56924i	0.892497	+	0.392771i
$477$	14.4838	−	11.1237i	0.663169	−	0.509319i
$478$	−5.89171	−	9.02983i	−0.269481	−	0.413015i
$479$	18.1416			0.828912			0.414456	−	0.910069i	$-0.363972\pi$
$479$	18.1416			0.828912			0.414456	+	0.910069i	$0.363972\pi$
$480$	8.73943	−	4.42972i	0.398899	−	0.202188i
$481$	1.87936			0.0856913
$482$	−5.32707	−	8.16444i	−0.242641	−	0.371880i
$483$	18.6832	+	1.22054i	0.850113	+	0.0555364i
$484$	−39.8823	−	17.5514i	−1.81283	−	0.797792i
$485$	−4.99526	+	4.99526i	−0.226823	+	0.226823i
$486$	21.3495	−	5.49541i	0.968432	−	0.249277i
$487$	17.2179			0.780218			0.390109	−	0.920769i	$-0.372437\pi$
$487$	17.2179			0.780218			0.390109	+	0.920769i	$0.372437\pi$
$488$	17.4890	−	24.4014i	0.791691	−	1.10460i
$489$	25.7092	−	22.5561i	1.16261	−	1.02002i
$490$	−2.14188	−	0.450455i	−0.0967605	−	0.0203495i
$491$	9.13362	+	9.13362i	0.412195	+	0.412195i	0.882502	−	0.470308i	$-0.155857\pi$
$491$	9.13362	+	9.13362i	0.412195	+	0.412195i	−0.470308	+	0.882502i	$0.655857\pi$
$492$	−3.87617	−	2.01704i	−0.174751	−	0.0909352i
$493$	−19.5517	+	19.5517i	−0.880564	+	0.880564i
$494$	−5.14804	−	7.89005i	−0.231621	−	0.354990i
$495$	−17.0319	−	2.23487i	−0.765528	−	0.100450i
$496$	19.5322	−	17.8938i	0.877022	−	0.803454i
$497$			21.9896i			0.986368i
$498$	−3.02132	+	10.8107i	−0.135389	+	0.484438i
$499$	−10.6968	−	10.6968i	−0.478856	−	0.478856i	0.425909	−	0.904766i	$-0.359954\pi$
$499$	−10.6968	−	10.6968i	−0.478856	−	0.478856i	−0.904766	+	0.425909i	$0.859954\pi$
$500$	−1.86406	+	0.724767i	−0.0833632	+	0.0324126i
$501$	8.08216	+	0.527993i	0.361084	+	0.0235890i
$502$	7.98768	−	37.9809i	0.356508	−	1.69517i
$503$		−	19.7936i		−	0.882554i	−0.897371	−	0.441277i	$-0.854526\pi$
$503$		−	19.7936i		−	0.882554i	0.897371	−	0.441277i	$-0.145474\pi$
$504$	19.8025	−	0.655021i	0.882073	−	0.0291770i
$505$		−	1.66035i		−	0.0738846i
$506$	−36.6851	−	7.71517i	−1.63085	−	0.342981i
$507$	−20.0637	−	1.31072i	−0.891059	−	0.0582113i
$508$	−5.31876	−	2.34068i	−0.235982	−	0.103851i
$509$	22.4663	+	22.4663i	0.995800	+	0.995800i	0.999991	−	0.00419119i	$-0.00133410\pi$
$509$	22.4663	+	22.4663i	0.995800	+	0.995800i	−0.00419119	+	0.999991i	$0.501334\pi$
$510$	−10.7467	−	3.00345i	−0.475873	−	0.132995i
$511$			1.01591i			0.0449414i
$512$	19.9584	−	10.6612i	0.882046	−	0.471164i
$513$	−24.3879	+	16.3182i	−1.07675	+	0.720465i
$514$	−0.747013	+	0.487405i	−0.0329493	+	0.0214985i
$515$	6.89765	−	6.89765i	0.303947	−	0.303947i
$516$	24.1055	−	7.60456i	1.06119	−	0.334772i
$517$	−14.9495	−	14.9495i	−0.657479	−	0.657479i
$518$	1.08274	−	5.14836i	0.0475729	−	0.226206i
$519$	15.3633	−	13.4791i	0.674373	−	0.591665i
$520$	−0.543215	−	3.29200i	−0.0238215	−	0.144364i
$521$	−26.0736			−1.14231			−0.571153	−	0.820844i	$-0.693504\pi$
$521$	−26.0736			−1.14231			−0.571153	+	0.820844i	$0.693504\pi$
$522$	−8.53337	+	24.2966i	−0.373496	+	1.06343i
$523$	−26.7306	+	26.7306i	−1.16885	+	1.16885i	−0.186365	+	0.982480i	$0.559671\pi$
$523$	−26.7306	+	26.7306i	−1.16885	+	1.16885i	−0.982480	+	0.186365i	$0.940329\pi$
$524$	−0.786667	−	2.02326i	−0.0343657	−	0.0883866i
$525$	−4.03577	−	0.263650i	−0.176136	−	0.0115066i
$526$	30.8627	−	20.1371i	1.34568	−	0.878017i
$527$	−30.1679			−1.31414
$528$	−39.4353	−	4.31499i	−1.71620	−	0.187786i
$529$	1.56878			0.0682078
$530$	−7.21001	+	4.70433i	−0.313183	+	0.204343i
$531$	20.9465	+	27.2738i	0.908999	+	1.18358i
$532$	−24.5801	+	9.55702i	−1.06568	+	0.414349i
$533$	−1.05216	+	1.05216i	−0.0455741	+	0.0455741i
$534$	5.07919	−	2.86030i	0.219798	−	0.123777i
$535$	−11.5249			−0.498265
$536$	9.29023	+	6.65852i	0.401277	+	0.287604i
$537$	18.2330	+	20.7817i	0.786810	+	0.896797i
$538$	−5.91189	+	28.1106i	−0.254880	+	1.21193i
$539$	6.26633	+	6.26633i	0.269910	+	0.269910i
$540$	−10.2334	+	1.81059i	−0.440374	+	0.0779152i
$541$	−5.28038	+	5.28038i	−0.227021	+	0.227021i	−0.811447	−	0.584426i	$-0.801320\pi$
$541$	−5.28038	+	5.28038i	−0.227021	+	0.227021i	0.584426	+	0.811447i	$0.301320\pi$
$542$	10.8964	−	7.10957i	0.468039	−	0.305382i
$543$	24.8254	−	21.7807i	1.06536	−	0.934699i
$544$	−24.9618	−	6.40139i	−1.07023	−	0.274457i
$545$		−	16.0438i		−	0.687242i
$546$	1.81605	−	6.49807i	0.0777200	−	0.278092i
$547$	12.7903	+	12.7903i	0.546874	+	0.546874i	0.925535	−	0.378661i	$-0.123616\pi$
$547$	12.7903	+	12.7903i	0.546874	+	0.546874i	−0.378661	+	0.925535i	$0.623616\pi$
$548$	3.17448	−	7.21342i	0.135607	−	0.308142i
$549$	−25.2542	+	19.3954i	−1.07782	+	0.827776i
$550$	7.92440	+	1.66656i	0.337897	+	0.0710625i
$551$		−	34.2768i		−	1.46024i
$552$	−22.5698	+	2.22581i	−0.960634	+	0.0947368i
$553$		−	36.6586i		−	1.55888i
$554$	−2.39235	+	11.3755i	−0.101641	+	0.483298i
$555$	−0.179886	+	2.75357i	−0.00763574	+	0.116883i
$556$	8.90193	+	22.8952i	0.377526	+	0.970974i
$557$	−24.2208	−	24.2208i	−1.02627	−	1.02627i	−0.999646	−	0.0266206i	$-0.991525\pi$
$557$	−24.2208	−	24.2208i	−1.02627	−	1.02627i	−0.0266206	−	0.999646i	$-0.508475\pi$
$558$	−25.3281	+	12.1612i	−1.07222	+	0.514825i
$559$		−	8.60748i		−	0.364058i
$560$	−9.33115	−	0.408503i	−0.394313	−	0.0172624i
$561$	29.7962	+	33.9614i	1.25800	+	1.43385i
$562$	13.6443	+	20.9117i	0.575551	+	0.882108i
$563$	−8.38227	+	8.38227i	−0.353270	+	0.353270i	−0.861325	−	0.508055i	$-0.830365\pi$
$563$	−8.38227	+	8.38227i	−0.353270	+	0.353270i	0.508055	+	0.861325i	$0.330365\pi$
$564$	−11.3461	−	5.90418i	−0.477758	−	0.248611i
$565$	9.45379	+	9.45379i	0.397724	+	0.397724i
$566$	21.6187	+	4.54658i	0.908700	+	0.191107i
$567$	−20.3038	−	5.42173i	−0.852679	−	0.227691i
$568$	−4.33660	−	26.2808i	−0.181960	−	1.10272i
$569$	16.2033			0.679277			0.339639	−	0.940556i	$-0.389695\pi$
$569$	16.2033			0.679277			0.339639	+	0.940556i	$0.389695\pi$
$570$	12.0530	−	6.78752i	0.504844	−	0.284298i
$571$	26.8812	−	26.8812i	1.12494	−	1.12494i	0.133955	−	0.990987i	$-0.457232\pi$
$571$	26.8812	−	26.8812i	1.12494	−	1.12494i	0.990987	−	0.133955i	$-0.0427678\pi$
$572$	−5.44149	+	12.3648i	−0.227520	+	0.516996i
$573$	1.56474	−	23.9520i	0.0653680	−	1.00061i
$574$	2.27614	+	3.48849i	0.0950043	+	0.145607i
$575$	4.62939			0.193059
$576$	−23.5377	+	4.68812i	−0.980736	+	0.195338i
$577$	−32.6853			−1.36071			−0.680354	−	0.732884i	$-0.738174\pi$
$577$	−32.6853			−1.36071			−0.680354	+	0.732884i	$0.738174\pi$
$578$	2.89963	+	4.44406i	0.120609	+	0.184849i
$579$	2.37910	−	36.4176i	0.0988720	−	1.51347i
$580$	4.88976	−	11.1111i	0.203036	−	0.461362i
$581$	7.56631	−	7.56631i	0.313903	−	0.313903i
$582$	15.0777	−	8.49086i	0.624991	−	0.351957i
$583$	34.8568			1.44362
$584$	−0.200350	−	1.21417i	−0.00829054	−	0.0502425i
$585$	−0.460417	+	3.50884i	−0.0190359	+	0.145073i
$586$	25.5813	+	5.37995i	1.05675	+	0.222244i
$587$	17.2406	+	17.2406i	0.711594	+	0.711594i	0.966869	−	0.255274i	$-0.0821658\pi$
$587$	17.2406	+	17.2406i	0.711594	+	0.711594i	−0.255274	+	0.966869i	$0.582166\pi$
$588$	4.75591	+	2.47483i	0.196130	+	0.102060i
$589$	26.4443	−	26.4443i	1.08962	−	1.08962i
$590$	−8.85849	−	13.5768i	−0.364698	−	0.558949i
$591$	−2.14144	−	2.44079i	−0.0880873	−	0.100401i
$592$	−0.278718	+	6.36656i	−0.0114552	+	0.261664i
$593$		−	24.4626i		−	1.00456i	−0.864705	−	0.502279i	$-0.832495\pi$
$593$		−	24.4626i		−	1.00456i	0.864705	−	0.502279i	$-0.167505\pi$
$594$	38.7064	+	16.5016i	1.58814	+	0.677067i
$595$	7.52156	+	7.52156i	0.308354	+	0.308354i
$596$	−8.52967	−	21.9378i	−0.349389	−	0.898608i
$597$	−0.905503	+	13.8608i	−0.0370598	+	0.567286i
$598$	−1.58944	+	7.55769i	−0.0649972	+	0.309057i
$599$		−	4.30406i		−	0.175859i	−0.996127	−	0.0879296i	$-0.971975\pi$
$599$		−	4.30406i		−	0.175859i	0.996127	−	0.0879296i	$-0.0280250\pi$
$600$	4.87533	−	0.480800i	0.199034	−	0.0196286i
$601$		−	33.9956i		−	1.38671i	−0.720597	−	0.693354i	$-0.756132\pi$
$601$		−	33.9956i		−	1.38671i	0.720597	−	0.693354i	$-0.243868\pi$
$602$	−23.5795	−	4.95897i	−0.961031	−	0.202112i
$603$	−7.38433	−	9.61491i	−0.300713	−	0.391549i
$604$	−6.52644	+	14.8301i	−0.265557	+	0.603429i
$605$	−15.4056	−	15.4056i	−0.626325	−	0.626325i
$606$	−1.09468	+	3.91691i	−0.0444685	+	0.159114i
$607$			38.0508i			1.54443i	0.635359	+	0.772217i	$0.280852\pi$
$607$			38.0508i			1.54443i	−0.635359	+	0.772217i	$0.719148\pi$
$608$	27.4920	−	16.2695i	1.11495	−	0.659815i
$609$	18.4528	−	16.1897i	0.747746	−	0.656040i
$610$	12.5715	−	8.20253i	0.509004	−	0.332111i
$611$	−3.07983	+	3.07983i	−0.124597	+	0.124597i
$612$	23.3723	+	14.1708i	0.944770	+	0.572822i
$613$	2.96495	+	2.96495i	0.119753	+	0.119753i	0.764444	−	0.644690i	$-0.223014\pi$
$613$	2.96495	+	2.96495i	0.119753	+	0.119753i	−0.644690	+	0.764444i	$0.723014\pi$
$614$	1.86940	−	8.88889i	0.0754430	−	0.358726i
$615$	−1.44088	−	1.64230i	−0.0581019	−	0.0662239i
$616$	30.7373	+	22.0302i	1.23844	+	0.887620i
$617$	−0.422670			−0.0170161			−0.00850803	−	0.999964i	$-0.502708\pi$
$617$	−0.422670			−0.0170161			−0.00850803	+	0.999964i	$0.502708\pi$
$618$	−20.8199	+	11.7245i	−0.837498	+	0.471629i
$619$	0.512577	−	0.512577i	0.0206022	−	0.0206022i	−0.696731	−	0.717333i	$-0.745363\pi$
$619$	0.512577	−	0.512577i	0.0206022	−	0.0206022i	0.717333	+	0.696731i	$0.245363\pi$
$620$	12.3445	−	4.79968i	0.495767	−	0.192760i
$621$	23.5958	+	4.67773i	0.946867	+	0.187711i
$622$	−7.83038	+	5.10910i	−0.313970	+	0.204856i
$623$	−5.55679			−0.222628
$624$	−0.888955	+	8.12428i	−0.0355867	+	0.325232i
$625$	−1.00000			−0.0400000
$626$	−5.81055	+	3.79122i	−0.232236	+	0.151528i
$627$	−55.8879	−	3.65106i	−2.23195	−	0.145809i
$628$	2.88266	+	7.41404i	0.115031	+	0.295853i
$629$	5.13189	−	5.13189i	0.204622	−	0.204622i
$630$	9.34693	+	3.28280i	0.372391	+	0.130790i
$631$	−41.2239			−1.64110			−0.820550	−	0.571575i	$-0.806332\pi$
$631$	−41.2239			−1.64110			−0.820550	+	0.571575i	$0.806332\pi$
$632$	7.22949	+	43.8123i	0.287573	+	1.74276i
$633$	16.9313	−	14.8548i	0.672958	−	0.590424i
$634$	2.05163	−	9.75534i	0.0814805	−	0.387434i
$635$	−2.05451	−	2.05451i	−0.0815306	−	0.0815306i
$636$	20.1107	−	6.34432i	0.797441	−	0.251569i
$637$	1.29096	−	1.29096i	0.0511497	−	0.0511497i
$638$	−41.1637	+	26.8582i	−1.62969	+	1.06333i
$639$	−3.67561	+	28.0118i	−0.145405	+	1.10813i
$640$	11.2326	−	1.35199i	0.444009	−	0.0534420i
$641$		−	25.6742i		−	1.01407i	−0.861926	−	0.507035i	$-0.830742\pi$
$641$		−	25.6742i		−	1.01407i	0.861926	−	0.507035i	$-0.169258\pi$
$642$	27.1883	+	7.59847i	1.07304	+	0.299888i
$643$	−10.3387	−	10.3387i	−0.407717	−	0.407717i	0.473225	−	0.880942i	$-0.343090\pi$
$643$	−10.3387	−	10.3387i	−0.407717	−	0.407717i	−0.880942	+	0.473225i	$0.843090\pi$
$644$	19.7880	+	8.70832i	0.779757	+	0.343156i
$645$	12.6114	+	0.823880i	0.496573	+	0.0324403i
$646$	−35.6026	−	7.48751i	−1.40077	−	0.294592i
$647$			4.44482i			0.174744i	0.996176	+	0.0873720i	$0.0278469\pi$
$647$			4.44482i			0.174744i	−0.996176	+	0.0873720i	$0.972153\pi$
$648$	25.3352	+	2.47562i	0.995260	+	0.0972514i
$649$			65.6371i			2.57648i
$650$	0.343338	−	1.63255i	0.0134668	−	0.0640338i
$651$	26.7264	+	1.74599i	1.04749	+	0.0684307i
$652$	36.8081	−	14.3114i	1.44152	−	0.560477i
$653$	−3.67007	−	3.67007i	−0.143621	−	0.143621i	0.631640	−	0.775261i	$-0.282382\pi$
$653$	−3.67007	−	3.67007i	−0.143621	−	0.143621i	−0.775261	+	0.631640i	$0.782382\pi$
$654$	−10.5779	+	37.8489i	−0.413627	+	1.48001i
$655$		−	1.08541i		−	0.0424103i
$656$	−3.40829	−	3.72037i	−0.133071	−	0.145256i
$657$	−0.169812	+	1.29414i	−0.00662501	+	0.0504891i
$658$	6.66260	+	10.2113i	0.259735	+	0.398079i
$659$	−0.132121	+	0.132121i	−0.00514672	+	0.00514672i	−0.709675	−	0.704529i	$-0.751158\pi$
$659$	−0.132121	+	0.132121i	−0.00514672	+	0.00514672i	0.704529	+	0.709675i	$0.251158\pi$
$660$	−17.5956	−	9.15620i	−0.684907	−	0.356405i
$661$	−34.7392	−	34.7392i	−1.35120	−	1.35120i	−0.884324	−	0.466874i	$-0.845380\pi$
$661$	−34.7392	−	34.7392i	−1.35120	−	1.35120i	−0.466874	−	0.884324i	$-0.654620\pi$
$662$	−6.18543	−	1.30084i	−0.240403	−	0.0505588i
$663$	6.99656	−	6.13848i	0.271724	−	0.238399i
$664$	−7.55067	+	10.5350i	−0.293023	+	0.408837i
$665$	−13.1863			−0.511344
$666$	2.23982	−	6.37733i	0.0867914	−	0.247116i
$667$	−19.8690	+	19.8690i	−0.769331	+	0.769331i
$668$	8.56011	+	3.76714i	0.331201	+	0.145755i
$669$	18.0948	+	1.18210i	0.699586	+	0.0457027i
$670$	3.12291	+	4.78628i	0.120649	+	0.184910i
$671$	−60.7767			−2.34626
$672$	21.7437	+	7.11581i	0.838782	+	0.274498i
$673$	−17.7433			−0.683955			−0.341978	−	0.939708i	$-0.611097\pi$
$673$	−17.7433			−0.683955			−0.341978	+	0.939708i	$0.611097\pi$
$674$	21.0532	+	32.2668i	0.810938	+	1.24287i
$675$	−5.09696	−	1.01044i	−0.196182	−	0.0388919i
$676$	−21.2502	−	9.35178i	−0.817314	−	0.359684i
$677$	−24.6454	+	24.6454i	−0.947201	+	0.947201i	−0.998674	−	0.0514738i	$-0.983608\pi$
$677$	−24.6454	+	24.6454i	−0.947201	+	0.947201i	0.0514738	+	0.998674i	$0.483608\pi$
$678$	−16.0694	−	28.5353i	−0.617141	−	1.09589i
$679$	−16.4955			−0.633038
$680$	−10.4727	−	7.50601i	−0.401609	−	0.287842i
$681$	−14.7756	−	16.8410i	−0.566201	−	0.645350i
$682$	−52.4783	−	11.0366i	−2.00950	−	0.422614i
$683$	−13.7216	−	13.7216i	−0.525042	−	0.525042i	0.394048	−	0.919090i	$-0.371074\pi$
$683$	−13.7216	−	13.7216i	−0.525042	−	0.525042i	−0.919090	+	0.394048i	$0.871074\pi$
$684$	−32.9092	+	8.06573i	−1.25831	+	0.308401i
$685$	2.78637	−	2.78637i	0.106462	−	0.106462i
$686$	−15.4241	−	23.6394i	−0.588893	−	0.902557i
$687$	−7.74511	+	6.79522i	−0.295494	+	0.259254i
$688$	29.1589	+	1.27653i	1.11167	+	0.0486673i
$689$		−	7.18103i		−	0.273576i
$690$	−10.9211	−	3.05220i	−0.415761	−	0.116195i
$691$	22.7012	+	22.7012i	0.863593	+	0.863593i	0.991753	−	0.128160i	$-0.0409072\pi$
$691$	22.7012	+	22.7012i	0.863593	+	0.863593i	−0.128160	+	0.991753i	$0.540907\pi$
$692$	21.9958	−	8.55220i	0.836153	−	0.325106i
$693$	−24.4315	−	31.8116i	−0.928078	−	1.20842i
$694$	0.826686	−	3.93083i	0.0313806	−	0.149212i
$695$			12.2825i			0.465901i
$696$	−18.8610	+	22.9881i	−0.714925	+	0.871363i
$697$			5.74619i			0.217652i
$698$	−30.8445	−	6.48684i	−1.16748	−	0.245531i
$699$	−1.36561	+	20.9038i	−0.0516521	+	0.790655i
$700$	−4.27443	−	1.88110i	−0.161558	−	0.0710987i
$701$	13.0196	+	13.0196i	0.491742	+	0.491742i	0.908855	−	0.417113i	$-0.136958\pi$
$701$	13.0196	+	13.0196i	0.491742	+	0.491742i	−0.417113	+	0.908855i	$0.636958\pi$
$702$	3.39957	−	7.97411i	0.128309	−	0.300963i
$703$			8.99692i			0.339325i
$704$	−41.0802	−	20.2675i	−1.54827	−	0.763859i
$705$	−4.21767	−	4.80726i	−0.158847	−	0.181052i
$706$	−16.5285	+	10.7844i	−0.622059	+	0.405876i
$707$	2.74142	−	2.74142i	0.103102	−	0.103102i
$708$	11.9467	+	37.8694i	0.448983	+	1.42322i
$709$	30.9405	+	30.9405i	1.16200	+	1.16200i	0.984038	+	0.177958i	$0.0569490\pi$
$709$	30.9405	+	30.9405i	1.16200	+	1.16200i	0.177958	+	0.984038i	$0.443051\pi$
$710$	2.74094	−	13.0330i	0.102866	−	0.489119i
$711$	6.12756	−	46.6981i	0.229801	−	1.75131i
$712$	6.64116	−	1.09586i	0.248888	−	0.0410691i
$713$	−30.6575			−1.14813
$714$	−12.7850	−	22.7031i	−0.478467	−	0.849641i
$715$	−4.77620	+	4.77620i	−0.178620	+	0.178620i
$716$	11.5685	+	29.7534i	0.432334	+	1.11194i
$717$	−0.860832	+	13.1770i	−0.0321484	+	0.492105i
$718$	20.4169	−	13.3215i	0.761953	−	0.497153i
$719$	10.7191			0.399755			0.199877	−	0.979821i	$-0.435946\pi$
$719$	10.7191			0.399755			0.199877	+	0.979821i	$0.435946\pi$
$720$	−11.8183	−	2.08010i	−0.440444	−	0.0775207i
$721$	22.7776			0.848280
$722$	15.2679	−	9.96188i	0.568213	−	0.370743i
$723$	−0.778333	+	11.9142i	−0.0289465	+	0.443093i
$724$	35.5427	−	13.8194i	1.32094	−	0.513595i
$725$	4.29193	−	4.29193i	0.159398	−	0.159398i
$726$	26.1861	+	46.5001i	0.971857	+	1.72578i
$727$	−11.9145			−0.441883			−0.220942	−	0.975287i	$-0.570913\pi$
$727$	−11.9145			−0.441883			−0.220942	+	0.975287i	$0.570913\pi$
$728$	4.53855	−	6.33237i	0.168210	−	0.234693i
$729$	−24.9580	−	10.3004i	−0.924371	−	0.381495i
$730$	0.126631	−	0.602120i	0.00468681	−	0.0222855i
$731$	−23.5041	−	23.5041i	−0.869332	−	0.869332i
$732$	−35.0652	+	11.0620i	−1.29605	+	0.408864i
$733$	−2.21674	+	2.21674i	−0.0818772	+	0.0818772i	−0.746859	−	0.664982i	$-0.768439\pi$
$733$	−2.21674	+	2.21674i	−0.0818772	+	0.0818772i	0.664982	+	0.746859i	$0.268439\pi$
$734$	32.5484	−	21.2369i	1.20138	−	0.783868i
$735$	1.76791	+	2.01504i	0.0652102	+	0.0743258i
$736$	−25.3669	−	6.50528i	−0.935037	−	0.239788i
$737$		−	23.1392i		−	0.852345i
$738$	2.31639	+	4.82432i	0.0852674	+	0.177586i
$739$	−12.7235	−	12.7235i	−0.468040	−	0.468040i	0.433239	−	0.901279i	$-0.357371\pi$
$739$	−12.7235	−	12.7235i	−0.468040	−	0.468040i	−0.901279	+	0.433239i	$0.857371\pi$
$740$	−1.28345	+	2.91641i	−0.0471807	+	0.107209i
$741$	−0.752174	+	11.5138i	−0.0276318	+	0.422969i
$742$	−19.6719	−	4.13716i	−0.722178	−	0.151880i
$743$			42.5407i			1.56067i	0.625365	+	0.780333i	$0.284950\pi$
$743$			42.5407i			1.56067i	−0.625365	+	0.780333i	$0.715050\pi$
$744$	−32.2863	+	3.18404i	−1.18367	+	0.116733i
$745$		−	11.7688i		−	0.431177i
$746$	8.97840	−	42.6917i	0.328722	−	1.56305i
$747$	10.9032	−	8.37373i	0.398926	−	0.306379i
$748$	18.9051	+	48.6228i	0.691239	+	1.77783i
$749$	−19.0289	−	19.0289i	−0.695300	−	0.695300i
$750$	2.35909	+	0.659309i	0.0861418	+	0.0240746i
$751$		−	6.32333i		−	0.230742i	−0.993322	−	0.115371i	$-0.963194\pi$
$751$		−	6.32333i		−	0.230742i	0.993322	−	0.115371i	$-0.0368056\pi$
$752$	−9.97656	−	10.8901i	−0.363808	−	0.397120i
$753$	−35.7316	+	31.3493i	−1.30213	+	1.14243i
$754$	5.53320	+	8.48036i	0.201507	+	0.308837i
$755$	−5.72851	+	5.72851i	−0.208482	+	0.208482i
$756$	−19.8859	−	13.9069i	−0.723243	−	0.505790i
$757$	−31.1767	−	31.1767i	−1.13314	−	1.13314i	−0.989652	−	0.143486i	$-0.954169\pi$
$757$	−31.1767	−	31.1767i	−1.13314	−	1.13314i	−0.143486	−	0.989652i	$-0.545831\pi$
$758$	4.07039	+	0.856035i	0.147843	+	0.0310926i
$759$	30.2798	+	34.5125i	1.09909	+	1.25273i
$760$	15.7596	−	2.60049i	0.571660	−	0.0943298i
$761$	43.3580			1.57172			0.785862	−	0.618401i	$-0.212219\pi$
$761$	43.3580			1.57172			0.785862	+	0.618401i	$0.212219\pi$
$762$	3.49221	+	6.20132i	0.126510	+	0.224650i
$763$	26.4901	−	26.4901i	0.959007	−	0.959007i
$764$	11.1642	−	25.3684i	0.403905	−	0.917798i
$765$	8.32420	+	10.8387i	0.300962	+	0.391874i
$766$	17.1928	+	26.3502i	0.621200	+	0.952071i
$767$	13.5222			0.488260
$768$	−27.3902	−	4.21632i	−0.988358	−	0.152143i
$769$	4.36961			0.157572			0.0787860	−	0.996892i	$-0.474896\pi$
$769$	4.36961			0.157572			0.0787860	+	0.996892i	$0.474896\pi$
$770$	10.3324	+	15.8357i	0.372353	+	0.570680i
$771$	1.09010	+	0.0712143i	0.0392590	+	0.00256472i
$772$	16.9745	−	38.5713i	0.610924	−	1.38821i
$773$	−34.9061	+	34.9061i	−1.25548	+	1.25548i	−0.302258	+	0.953226i	$0.597741\pi$
$773$	−34.9061	+	34.9061i	−1.25548	+	1.25548i	−0.953226	+	0.302258i	$0.902259\pi$
$774$	−29.2082	−	10.2584i	−1.04987	−	0.368731i
$775$	6.62238			0.237883
$776$	19.7145	−	3.25309i	0.707708	−	0.116779i
$777$	−4.84346	+	4.24944i	−0.173758	+	0.152448i
$778$	−28.0892	−	5.90738i	−1.00705	−	0.211790i
$779$	−5.03693	−	5.03693i	−0.180467	−	0.180467i
$780$	−1.88632	+	3.62496i	−0.0675410	+	0.129794i
$781$	−38.1294	+	38.1294i	−1.36438	+	1.36438i
$782$	16.2973	+	24.9777i	0.582789	+	0.893202i
$783$	26.2126	−	17.5391i	0.936760	−	0.626795i
$784$	4.18183	+	4.56475i	0.149351	+	0.163027i
$785$			3.97737i			0.141958i
$786$	−0.715619	+	2.56057i	−0.0255253	+	0.0913326i
$787$	1.53303	+	1.53303i	0.0546467	+	0.0546467i	0.733902	−	0.679255i	$-0.237697\pi$
$787$	1.53303	+	1.53303i	0.0546467	+	0.0546467i	−0.679255	+	0.733902i	$0.737697\pi$
$788$	−1.35871	−	3.49451i	−0.0484019	−	0.124487i
$789$	−45.0373	−	2.94221i	−1.60337	−	0.104745i
$790$	−4.56938	+	21.7271i	−0.162571	+	0.773015i
$791$			31.2185i			1.11000i
$792$	35.4728	+	33.2013i	1.26047	+	1.17976i
$793$			12.5209i			0.444631i
$794$	−18.0292	−	3.79169i	−0.639833	−	0.134562i
$795$	10.5214	+	0.687345i	0.373156	+	0.0243776i
$796$	−6.46060	+	14.6805i	−0.228990	+	0.520337i
$797$	−0.378298	−	0.378298i	−0.0134000	−	0.0134000i	0.700375	−	0.713775i	$-0.253016\pi$
$797$	−0.378298	−	0.378298i	−0.0134000	−	0.0134000i	−0.713775	+	0.700375i	$0.753016\pi$
$798$	31.1078	+	8.69387i	1.10120	+	0.307760i
$799$			16.8200i			0.595047i
$800$	5.47954	+	1.40521i	0.193731	+	0.0496818i
$801$	−7.07859	−	0.928828i	−0.250110	−	0.0328185i
$802$	11.0449	−	7.20651i	0.390010	−	0.254471i
$803$	−1.76157	+	1.76157i	−0.0621645	+	0.0621645i
$804$	−4.21160	−	13.3502i	−0.148532	−	0.470826i
$805$	7.64363	+	7.64363i	0.269402	+	0.269402i
$806$	−2.27371	+	10.8113i	−0.0800881	+	0.380813i
$807$	26.4459	−	23.2024i	0.930938	−	0.816764i
$808$	−2.73575	+	3.81703i	−0.0962435	+	0.134283i
$809$	−34.6827			−1.21938			−0.609690	−	0.792640i	$-0.708706\pi$
$809$	−34.6827			−1.21938			−0.609690	+	0.792640i	$0.708706\pi$
$810$	11.3580	+	5.74420i	0.399079	+	0.201831i
$811$	8.24229	−	8.24229i	0.289426	−	0.289426i	−0.547427	−	0.836853i	$-0.684393\pi$
$811$	8.24229	−	8.24229i	0.289426	−	0.289426i	0.836853	+	0.547427i	$0.184393\pi$
$812$	26.4191	−	10.2720i	0.927129	−	0.360478i
$813$	−15.9008	−	1.03877i	−0.557666	−	0.0364313i
$814$	10.8046	−	7.04968i	0.378700	−	0.247091i
$815$	19.7462			0.691679
$816$	19.7572	+	24.6121i	0.691642	+	0.861596i
$817$	41.2060			1.44162
$818$	−21.0750	+	13.7509i	−0.736871	+	0.480788i
$819$	−6.55367	+	5.03327i	−0.229004	+	0.175877i
$820$	−0.914211	−	2.35130i	−0.0319256	−	0.0821109i
$821$	−20.9859	+	20.9859i	−0.732412	+	0.732412i	−0.971097	−	0.238685i	$-0.923284\pi$
$821$	−20.9859	+	20.9859i	−0.732412	+	0.732412i	0.238685	+	0.971097i	$0.423284\pi$
$822$	−8.41037	+	4.73622i	−0.293345	+	0.165195i
$823$	−8.09445			−0.282155			−0.141077	−	0.989999i	$-0.545057\pi$
$823$	−8.09445			−0.282155			−0.141077	+	0.989999i	$0.545057\pi$
$824$	−27.2225	+	4.49199i	−0.948340	+	0.156486i
$825$	−6.54077	−	7.45510i	−0.227721	−	0.259553i
$826$	7.79047	−	37.0432i	0.271065	−	1.28890i
$827$	−1.90962	−	1.90962i	−0.0664038	−	0.0664038i	0.673125	−	0.739529i	$-0.264952\pi$
$827$	−1.90962	−	1.90962i	−0.0664038	−	0.0664038i	−0.739529	+	0.673125i	$0.764952\pi$
$828$	23.7516	+	14.4008i	0.825426	+	0.500463i
$829$	−16.7258	+	16.7258i	−0.580911	+	0.580911i	−0.935154	−	0.354242i	$-0.884739\pi$
$829$	−16.7258	+	16.7258i	−0.580911	+	0.580911i	0.354242	+	0.935154i	$0.384739\pi$
$830$	−5.42758	+	3.54134i	−0.188394	+	0.122922i
$831$	10.7018	−	9.38928i	0.371241	−	0.325711i
$832$	−4.17541	+	8.46315i	−0.144756	+	0.293407i
$833$		−	7.05035i		−	0.244280i
$834$	8.09795	−	28.9755i	0.280409	−	1.00334i
$835$	3.30656	+	3.30656i	0.114428	+	0.114428i
$836$	−59.1929	−	26.0497i	−2.04723	−	0.900946i
$837$	33.7540	+	6.69153i	1.16671	+	0.231293i
$838$	47.7267	+	10.0373i	1.64869	+	0.346733i
$839$			32.0878i			1.10779i	0.832586	+	0.553896i	$0.186860\pi$
$839$			32.0878i			1.10779i	−0.832586	+	0.553896i	$0.813140\pi$
$840$	8.84356	+	7.25585i	0.305132	+	0.250351i
$841$			7.84134i			0.270391i
$842$	10.8296	−	51.4940i	0.373213	−	1.77460i
$843$	1.99356	−	30.5160i	0.0686618	−	1.05103i
$844$	24.2407	−	9.42505i	0.834399	−	0.324424i
$845$	−8.20842	−	8.20842i	−0.282378	−	0.282378i
$846$	6.78041	+	14.1215i	0.233115	+	0.485507i
$847$		−	50.8725i		−	1.74800i
$848$	24.3267	+	1.06498i	0.835381	+	0.0365716i
$849$	−17.8440	−	20.3384i	−0.612404	−	0.698011i
$850$	−3.52040	−	5.39547i	−0.120749	−	0.185063i
$851$	5.21518	−	5.21518i	0.178774	−	0.178774i
$852$	−15.0589	+	28.9388i	−0.515909	+	0.991428i
$853$	17.1882	+	17.1882i	0.588513	+	0.588513i	0.937229	−	0.348716i	$-0.113382\pi$
$853$	17.1882	+	17.1882i	0.588513	+	0.588513i	−0.348716	+	0.937229i	$0.613382\pi$
$854$	34.3001	+	7.21359i	1.17373	+	0.246844i
$855$	−16.7976	−	2.20412i	−0.574466	−	0.0753794i
$856$	26.4950	+	18.9896i	0.905579	+	0.649049i
$857$	−6.92877			−0.236682			−0.118341	−	0.992973i	$-0.537758\pi$
$857$	−6.92877			−0.236682			−0.118341	+	0.992973i	$0.537758\pi$
$858$	14.4165	−	8.11851i	0.492171	−	0.277161i
$859$	−13.5608	+	13.5608i	−0.462688	+	0.462688i	−0.899536	−	0.436847i	$-0.856095\pi$
$859$	−13.5608	+	13.5608i	−0.462688	+	0.462688i	0.436847	+	0.899536i	$0.356095\pi$
$860$	13.3572	+	5.87824i	0.455476	+	0.200446i
$861$	0.332565	−	5.09067i	0.0113338	−	0.173490i
$862$	−3.96594	−	6.07833i	−0.135081	−	0.207029i
$863$	51.8572			1.76524			0.882620	−	0.470088i	$-0.155778\pi$
$863$	51.8572			1.76524			0.882620	+	0.470088i	$0.155778\pi$
$864$	26.5091	+	12.6991i	0.901859	+	0.432032i
$865$	11.7999			0.401210
$866$	−19.9589	−	30.5896i	−0.678230	−	1.03948i
$867$	0.423662	−	6.48512i	0.0143883	−	0.220246i
$868$	28.3069	+	12.4573i	0.960800	+	0.422829i
$869$	63.5651	−	63.5651i	2.15630	−	2.15630i
$870$	−12.9548	+	7.29535i	−0.439208	+	0.247335i
$871$	−4.76704			−0.161525
$872$	−26.4354	+	36.8837i	−0.895215	+	1.24904i
$873$	−21.0130	−	2.75725i	−0.711182	−	0.0933187i
$874$	−36.1804	−	7.60903i	−1.22382	−	0.257379i
$875$	−1.65111	−	1.65111i	−0.0558177	−	0.0558177i
$876$	−0.695717	+	1.33697i	−0.0235061	+	0.0451720i
$877$	−33.6449	+	33.6449i	−1.13611	+	1.13611i	−0.146968	+	0.989141i	$0.546951\pi$
$877$	−33.6449	+	33.6449i	−1.13611	+	1.13611i	−0.989141	+	0.146968i	$0.953049\pi$
$878$	5.07624	+	7.78001i	0.171315	+	0.262563i
$879$	−21.1147	−	24.0663i	−0.712182	−	0.811737i
$880$	−15.4717	−	16.8883i	−0.521550	−	0.569305i
$881$		−	19.3279i		−	0.651174i	−0.945512	−	0.325587i	$-0.894438\pi$
$881$		−	19.3279i		−	0.651174i	0.945512	−	0.325587i	$-0.105562\pi$
$882$	−2.84212	−	5.91926i	−0.0956990	−	0.199312i
$883$	10.3149	+	10.3149i	0.347125	+	0.347125i	0.859038	−	0.511912i	$-0.171063\pi$
$883$	10.3149	+	10.3149i	0.347125	+	0.347125i	−0.511912	+	0.859038i	$0.671063\pi$
$884$	10.0171	−	3.89474i	0.336910	−	0.130994i
$885$	−1.29431	+	19.8123i	−0.0435076	+	0.665985i
$886$	9.17614	−	43.6319i	0.308278	−	1.46584i
$887$		−	5.42448i		−	0.182136i	−0.995845	−	0.0910681i	$-0.970972\pi$
$887$		−	5.42448i		−	0.182136i	0.995845	−	0.0910681i	$-0.0290281\pi$
$888$	4.95060	−	6.03388i	0.166131	−	0.202484i
$889$		−	6.78443i		−	0.227543i
$890$	3.29344	+	0.692637i	0.110396	+	0.0232172i
$891$	−25.8051	−	44.6074i	−0.864504	−	1.49440i
$892$	19.1649	+	8.43408i	0.641687	+	0.282394i
$893$	−14.7439	−	14.7439i	−0.493384	−	0.493384i
$894$	−7.75931	+	27.7638i	−0.259510	+	0.928560i
$895$			15.9616i			0.533538i
$896$	20.7786	+	16.3140i	0.694164	+	0.545014i
$897$	7.11011	−	6.23810i	0.237400	−	0.208284i
$898$	23.3686	−	15.2474i	0.779820	−	0.508811i
$899$	−28.4228	+	28.4228i	−0.947953	+	0.947953i
$900$	−5.13062	−	3.11074i	−0.171021	−	0.103691i
$901$	−19.6090	−	19.6090i	−0.653270	−	0.653270i
$902$	−2.10218	+	9.99573i	−0.0699950	+	0.332821i
$903$	19.4625	+	22.1831i	0.647671	+	0.738208i
$904$	−6.15664	−	37.3106i	−0.204767	−	1.24093i
$905$	19.0674			0.633822
$906$	17.2909	−	9.73722i	0.574453	−	0.323497i
$907$	29.6790	−	29.6790i	0.985477	−	0.985477i	−0.0144194	−	0.999896i	$-0.504590\pi$
$907$	29.6790	−	29.6790i	0.985477	−	0.985477i	0.999896	+	0.0144194i	$0.00459001\pi$
$908$	−9.37482	−	24.1115i	−0.311114	−	0.800168i
$909$	3.95043	−	3.03396i	0.131027	−	0.100630i
$910$	3.26240	−	2.12863i	0.108148	−	0.0705633i
$911$	48.5376			1.60812			0.804061	−	0.594547i	$-0.202669\pi$
$911$	48.5376			1.60812			0.804061	+	0.594547i	$0.202669\pi$
$912$	−38.8928	−	4.25563i	−1.28787	−	0.140918i
$913$	26.2396			0.868404
$914$	30.3430	−	19.7979i	1.00366	−	0.654858i
$915$	−18.3453	−	1.19846i	−0.606475	−	0.0396200i
$916$	−11.0888	+	4.31143i	−0.366383	+	0.142454i
$917$	1.79213	−	1.79213i	0.0591812	−	0.0591812i
$918$	−12.4915	−	31.0577i	−0.412281	−	1.02506i
$919$	−20.9845			−0.692216			−0.346108	−	0.938195i	$-0.612497\pi$
$919$	−20.9845			−0.692216			−0.346108	+	0.938195i	$0.612497\pi$
$920$	−10.6426	−	7.62783i	−0.350878	−	0.251482i
$921$	−8.36247	+	7.33686i	−0.275553	+	0.241758i
$922$	−5.40725	+	25.7111i	−0.178078	+	0.846750i
$923$	7.85525	+	7.85525i	0.258559	+	0.258559i
$924$	−13.9344	−	44.1702i	−0.458407	−	1.45309i
$925$	−1.12654	+	1.12654i	−0.0370403	+	0.0370403i
$926$	−16.3233	+	10.6505i	−0.536418	+	0.349998i
$927$	29.0155	+	3.80731i	0.952995	+	0.125049i
$928$	−29.5489	+	17.4867i	−0.969990	+	0.574030i
$929$		−	23.9126i		−	0.784546i	−0.919849	−	0.392273i	$-0.871689\pi$
$929$		−	23.9126i		−	0.784546i	0.919849	−	0.392273i	$-0.128311\pi$
$930$	−15.6228	−	4.36619i	−0.512292	−	0.143173i
$931$	6.18012	+	6.18012i	0.202545	+	0.202545i
$932$	−9.74338	+	22.1400i	−0.319155	+	0.725220i
$933$	11.4267	+	0.746486i	0.374093	+	0.0244388i
$934$	−5.65433	−	1.18915i	−0.185015	−	0.0389102i
$935$			26.0844i			0.853051i
$936$	6.83997	−	7.30795i	0.223571	−	0.238868i
$937$		−	2.05837i		−	0.0672439i	−0.999435	−	0.0336219i	$-0.989296\pi$
$937$		−	2.05837i		−	0.0672439i	0.999435	−	0.0336219i	$-0.0107042\pi$
$938$	−2.74640	+	13.0589i	−0.0896731	+	0.426390i
$939$	8.47920	+	0.553931i	0.276708	+	0.0180769i
$940$	−2.67603	−	6.88260i	−0.0872825	−	0.224486i
$941$	26.4283	+	26.4283i	0.861538	+	0.861538i	0.991517	−	0.129979i	$-0.0414910\pi$
$941$	26.4283	+	26.4283i	0.861538	+	0.861538i	−0.129979	+	0.991517i	$0.541491\pi$
$942$	2.62231	−	9.38297i	0.0854396	−	0.305714i
$943$			5.83945i			0.190159i
$944$	−2.00541	+	45.8083i	−0.0652706	+	1.49093i
$945$	−6.74729	−	10.0840i	−0.219489	−	0.328032i
$946$	−32.2876	−	49.4851i	−1.04976	−	1.60890i
$947$	12.2254	−	12.2254i	0.397271	−	0.397271i	−0.479998	−	0.877270i	$-0.659363\pi$
$947$	12.2254	−	12.2254i	0.397271	−	0.397271i	0.877270	+	0.479998i	$0.159363\pi$
$948$	25.1045	−	48.2436i	0.815355	−	1.56688i
$949$	0.362911	+	0.362911i	0.0117806	+	0.0117806i
$950$	7.81538	+	1.64364i	0.253564	+	0.0533266i
$951$	−9.17761	+	8.05203i	−0.297604	+	0.261105i
$952$	−4.89830	−	29.6848i	−0.158755	−	0.962090i
$953$	3.93546			0.127482			0.0637411	−	0.997966i	$-0.479697\pi$
$953$	3.93546			0.127482			0.0637411	+	0.997966i	$0.479697\pi$
$954$	−24.3678	−	8.55837i	−0.788937	−	0.277088i
$955$	9.79921	−	9.79921i	0.317095	−	0.317095i
$956$	−6.14188	+	13.9563i	−0.198643	+	0.451378i
$957$	60.0693	+	3.92422i	1.94177	+	0.126852i
$958$	−14.0196	−	21.4869i	−0.452953	−	0.694211i
$959$	9.20120			0.297122
$960$	−12.0003	−	6.92774i	−0.387307	−	0.223592i
$961$	−12.8559			−0.414706
$962$	−1.45234	−	2.22591i	−0.0468254	−	0.0717662i
$963$	−21.0595	−	27.4209i	−0.678633	−	0.883627i
$964$	−5.55326	+	12.6187i	−0.178859	+	0.406422i
$965$	14.8991	−	14.8991i	0.479620	−	0.479620i
$966$	−12.9925	−	23.0715i	−0.418027	−	0.742314i
$967$	18.4417			0.593046			0.296523	−	0.955026i	$-0.404173\pi$
$967$	18.4417			0.593046			0.296523	+	0.955026i	$0.404173\pi$
$968$	10.0326	+	60.8000i	0.322461	+	1.95419i
$969$	29.3863	+	33.4942i	0.944024	+	1.07599i
$970$	9.77666	+	2.05611i	0.313910	+	0.0660177i
$971$	17.6241	+	17.6241i	0.565585	+	0.565585i	0.930888	−	0.365304i	$-0.119035\pi$
$971$	17.6241	+	17.6241i	0.565585	+	0.565585i	−0.365304	+	0.930888i	$0.619035\pi$
$972$	−23.0074	−	21.0395i	−0.737961	−	0.674843i
$973$	−20.2797	+	20.2797i	−0.650138	+	0.650138i
$974$	−13.3058	−	20.3929i	−0.426345	−	0.653430i
$975$	−1.53586	+	1.34750i	−0.0491870	+	0.0431545i
$976$	−42.4162	−	1.85691i	−1.35771	−	0.0594384i
$977$			2.74811i			0.0879199i	0.999033	+	0.0439600i	$0.0139974\pi$
$977$			2.74811i			0.0879199i	−0.999033	+	0.0439600i	$0.986003\pi$
$978$	−46.5831	−	13.0189i	−1.48956	−	0.416297i
$979$	−9.63534	−	9.63534i	−0.307947	−	0.307947i
$980$	1.12170	+	2.88495i	0.0358314	+	0.0921564i
$981$	38.1727	−	29.3170i	1.21876	−	0.936019i
$982$	3.75951	−	17.8762i	0.119971	−	0.570452i
$983$		−	40.7967i		−	1.30121i	−0.759415	−	0.650607i	$-0.774515\pi$
$983$		−	40.7967i		−	1.30121i	0.759415	−	0.650607i	$-0.225485\pi$
$984$	0.606475	+	6.14967i	0.0193337	+	0.196044i
$985$		−	1.87468i		−	0.0597322i
$986$	38.2663	+	8.04771i	1.21865	+	0.256291i
$987$	0.973466	−	14.9012i	0.0309858	−	0.474309i
$988$	−5.36663	+	12.1947i	−0.170735	+	0.387964i
$989$	−23.8856	−	23.8856i	−0.759517	−	0.759517i
$990$	10.5151	+	21.8997i	0.334191	+	0.696017i
$991$		−	6.87918i		−	0.218524i	−0.994013	−	0.109262i	$-0.965151\pi$
$991$		−	6.87918i		−	0.218524i	0.994013	−	0.109262i	$-0.0348488\pi$
$992$	−36.2876	−	9.30586i	−1.15213	−	0.295461i
$993$	5.10543	+	5.81912i	0.162016	+	0.184664i
$994$	26.0445	−	16.9933i	0.826080	−	0.538994i
$995$	−5.67072	+	5.67072i	−0.179774	+	0.179774i
$996$	15.1390	−	4.77590i	0.479697	−	0.151330i
$997$	−30.0974	−	30.0974i	−0.953196	−	0.953196i	0.0457571	−	0.998953i	$-0.485430\pi$
$997$	−30.0974	−	30.0974i	−0.953196	−	0.953196i	−0.998953	+	0.0457571i	$0.985430\pi$
$998$	−4.40295	+	20.9357i	−0.139373	+	0.662708i
$999$	−6.88022	+	4.60362i	−0.217680	+	0.145652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bk.b.11.12	✓	60
3.2	odd	2	inner	240.2.bk.b.11.19	yes	60
4.3	odd	2		960.2.bk.b.911.17		60
12.11	even	2		960.2.bk.b.911.2		60
16.3	odd	4	inner	240.2.bk.b.131.19	yes	60
16.13	even	4		960.2.bk.b.431.2		60
48.29	odd	4		960.2.bk.b.431.17		60
48.35	even	4	inner	240.2.bk.b.131.12	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bk.b.11.12	✓	60	1.1	even	1	trivial
240.2.bk.b.11.19	yes	60	3.2	odd	2	inner
240.2.bk.b.131.12	yes	60	48.35	even	4	inner
240.2.bk.b.131.19	yes	60	16.3	odd	4	inner
960.2.bk.b.431.2		60	16.13	even	4
960.2.bk.b.431.17		60	48.29	odd	4
960.2.bk.b.911.2		60	12.11	even	2
960.2.bk.b.911.17		60	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.772787 - 1.18440i) q^{2} +(-0.112911 + 1.72837i) q^{3} +(-0.805601 + 1.83058i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.13433 - 1.20193i) q^{6} -2.33502 q^{7} +(2.79069 - 0.460493i) q^{8} +(-2.97450 - 0.390304i) q^{9} +O(q^{10})\)	\(q+(-0.772787 - 1.18440i) q^{2} +(-0.112911 + 1.72837i) q^{3} +(-0.805601 + 1.83058i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.13433 - 1.20193i) q^{6} -2.33502 q^{7} +(2.79069 - 0.460493i) q^{8} +(-2.97450 - 0.390304i) q^{9} +(1.38394 + 0.291053i) q^{10} +(-4.04887 - 4.04887i) q^{11} +(-3.07294 - 1.59907i) q^{12} +(-0.834130 + 0.834130i) q^{13} +(1.80447 + 2.76560i) q^{14} +(-1.14230 - 1.30198i) q^{15} +(-2.70202 - 2.94943i) q^{16} +4.55545i q^{17} +(1.83638 + 3.82462i) q^{18} +(-3.99317 - 3.99317i) q^{19} +(-0.724767 - 1.86406i) q^{20} +(0.263650 - 4.03577i) q^{21} +(-1.66656 + 7.92440i) q^{22} +4.62939i q^{23} +(0.480800 + 4.87533i) q^{24} -1.00000i q^{25} +(1.63255 + 0.343338i) q^{26} +(1.01044 - 5.09696i) q^{27} +(1.88110 - 4.27443i) q^{28} +(4.29193 + 4.29193i) q^{29} +(-0.659309 + 2.35909i) q^{30} +6.62238i q^{31} +(-1.40521 + 5.47954i) q^{32} +(7.45510 - 6.54077i) q^{33} +(5.39547 - 3.52040i) q^{34} +(1.65111 - 1.65111i) q^{35} +(3.11074 - 5.13062i) q^{36} +(-1.12654 - 1.12654i) q^{37} +(-1.64364 + 7.81538i) q^{38} +(-1.34750 - 1.53586i) q^{39} +(-1.64770 + 2.29893i) q^{40} +1.26139 q^{41} +(-4.98371 + 2.80653i) q^{42} +(-5.15956 + 5.15956i) q^{43} +(10.6735 - 4.14999i) q^{44} +(2.37928 - 1.82730i) q^{45} +(5.48304 - 3.57753i) q^{46} +3.69227 q^{47} +(5.40278 - 4.33705i) q^{48} -1.54767 q^{49} +(-1.18440 + 0.772787i) q^{50} +(-7.87350 - 0.514362i) q^{51} +(-0.854962 - 2.19891i) q^{52} +(-4.30450 + 4.30450i) q^{53} +(-6.81769 + 2.74210i) q^{54} +5.72597 q^{55} +(-6.51632 + 1.07526i) q^{56} +(7.35254 - 6.45079i) q^{57} +(1.76661 - 8.40011i) q^{58} +(-8.10560 - 8.10560i) q^{59} +(3.30361 - 1.04219i) q^{60} +(7.50538 - 7.50538i) q^{61} +(7.84354 - 5.11769i) q^{62} +(6.94553 + 0.911368i) q^{63} +(7.57589 - 2.57018i) q^{64} -1.17964i q^{65} +(-13.5081 - 3.77519i) q^{66} +(2.85749 + 2.85749i) q^{67} +(-8.33911 - 3.66988i) q^{68} +(-8.00128 - 0.522709i) q^{69} +(-3.23153 - 0.679616i) q^{70} -9.41730i q^{71} +(-8.48064 + 0.280520i) q^{72} -0.435077i q^{73} +(-0.463696 + 2.20484i) q^{74} +(1.72837 + 0.112911i) q^{75} +(10.5267 - 4.09290i) q^{76} +(9.45421 + 9.45421i) q^{77} +(-0.777746 + 2.78287i) q^{78} +15.6995i q^{79} +(3.99617 + 0.174946i) q^{80} +(8.69533 + 2.32192i) q^{81} +(-0.974783 - 1.49398i) q^{82} +(-3.24036 + 3.24036i) q^{83} +(7.17539 + 3.73385i) q^{84} +(-3.22119 - 3.22119i) q^{85} +(10.0982 + 2.12373i) q^{86} +(-7.90264 + 6.93342i) q^{87} +(-13.1636 - 9.43467i) q^{88} +2.37976 q^{89} +(-4.00293 - 1.40590i) q^{90} +(1.94771 - 1.94771i) q^{91} +(-8.47444 - 3.72944i) q^{92} +(-11.4459 - 0.747740i) q^{93} +(-2.85333 - 4.37311i) q^{94} +5.64720 q^{95} +(-9.31199 - 3.04743i) q^{96} +7.06437 q^{97} +(1.19602 + 1.83306i) q^{98} +(10.4631 + 13.6237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

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